Differential and Riemannian geometry Books
World Scientific Publishing Co Pte Ltd Total Mean Curvature And Submanifolds Of Finite
Book SynopsisDuring the last four decades, there were numerous important developments on total mean curvature and the theory of finite type submanifolds. This unique and expanded second edition comprises a comprehensive account of the latest updates and new results that cover total mean curvature and submanifolds of finite type. The longstanding biharmonic conjecture of the author's and the generalized biharmonic conjectures are also presented in details. This book will be of use to graduate students and researchers in the field of geometry.Table of ContentsDifferentiable Manifolds; Riemannian and Pseudo-Riemannian Manifolds; Hodge Theory and Spectral Geometry; Submanifolds; Total Mean Curvature; Submanifolds of Finite Type; Biharmonic Submanifolds and Biharmonic Conjectures; lambda-biharmonic and Null 2-type Submanifolds; Applications of Finite Type Theory; Additional Topics in Finite Type Theory;
£42.75
World Scientific Publishing Co Pte Ltd Nonabelian Multiplicative Integration On Surfaces
Book SynopsisNonabelian multiplicative integration on curves is a classical theory. This volume is about the 2-dimensional case, which is much more difficult. In our construction, the setup is a Lie crossed module: there is a Lie group H, together with an action on it by another Lie group G. The multiplicative integral is an element of H, and it is the limit of Riemann products. Each Riemann product involves a fractal decomposition of the surface into kites (triangles with strings connecting them to the base point). There is a twisting of the integrand, that comes from a 1-dimensional multiplicative integral along the strings, with values in the group G.The main result of this work is the 3-dimensional nonabelian Stokes theorem. This result is new; only a special case of it was predicted (without proof) in papers in mathematical physics. Our constructions and proofs are of a straightforward nature. There are plenty of illustrations to clarify the geometric constructions.Our volume touches on some of the central issues (e.g., descent for nonabelian gerbes) in an unusually down-to-earth manner, involving analysis, differential geometry, combinatorics and Lie theory — instead of the 2-categories and 2-functors that other authors prefer.Table of ContentsIntroduction; Polyhedra and Piecewise Smooth Geometry; Estimates for the Nonabelian Exponential Map; Multiplicative Integration in Dimension 1; Multiplicative Integration in Dimension 2; Quasi Crossed Modules and Additive Feedback; Stokes Theorem in Dimension 2; Square Puzzles; Stokes Theorem in Dimension 3; Multiplicative Integration on Triangular Kites; References; Appendix: Lecture Notes (edited);
£55.10
World Scientific Publishing Co Pte Ltd Brief Introduction To Symplectic And Contact
Book SynopsisThe book introduces the basic notions in Symplectic and Contact Geometry at the level of the second year graduate student. It also contains many exercises, some of which are solved only in the last chapter.We begin with the linear theory, then give the definition of symplectic manifolds and some basic examples, review advanced calculus, discuss Hamiltonian systems, tour rapidly group and the basics of contact geometry, and solve problems in chapter 8. The material just described can be used as a one semester course on Symplectic and Contact Geometry.The book contains also more advanced material, suitable to advanced graduate students and researchers.
£58.90
World Scientific Publishing Co Pte Ltd Introduction To Modern Finsler Geometry
Book SynopsisThis comprehensive book is an introduction to the basics of Finsler geometry with recent developments in its area. It includes local geometry as well as global geometry of Finsler manifolds.In Part I, the authors discuss differential manifolds, Finsler metrics, the Chern connection, Riemannian and non-Riemannian quantities. Part II is written for readers who would like to further their studies in Finsler geometry. It covers projective transformations, comparison theorems, fundamental group, minimal immersions, harmonic maps, Einstein metrics, conformal transformations, amongst other related topics. The authors made great efforts to ensure that the contents are accessible to senior undergraduate students, graduate students, mathematicians and scientists.
£62.70
World Scientific Publishing Co Pte Ltd Introduction To Modern Finsler Geometry
Book SynopsisThis comprehensive book is an introduction to the basics of Finsler geometry with recent developments in its area. It includes local geometry as well as global geometry of Finsler manifolds.In Part I, the authors discuss differential manifolds, Finsler metrics, the Chern connection, Riemannian and non-Riemannian quantities. Part II is written for readers who would like to further their studies in Finsler geometry. It covers projective transformations, comparison theorems, fundamental group, minimal immersions, harmonic maps, Einstein metrics, conformal transformations, amongst other related topics. The authors made great efforts to ensure that the contents are accessible to senior undergraduate students, graduate students, mathematicians and scientists.
£38.00
World Scientific Publishing Co Pte Ltd Current Developments In Differential Geometry And
Book SynopsisThis volume contains contributions by the main participants of the 4th International Colloquium on Differential Geometry and its Related Fields (ICDG2014). These articles cover recent developments and are devoted mainly to the study of some geometric structures on manifolds and graphs. Readers will find a broad overview of differential geometry and its relationship to other fields in mathematics and physics.Table of ContentsPreface; Organizing Committees; Presentations; Einstein Metrics on the Symplectic Group Which are Not Naturally Reductive (Andreas Arvanitoyeorgos, Yusuke Sakane and Marina Statha); Laplacians for Finite Regular Kahler Graphs and for Their Dual Graphs (Toshiaki Adachi); S1-Invariant Einstein-Weyl Structure and Twistor Correspondence (Fuminori Nakata); A Family of Surfaces in E3 Given by an Over-Determined System (Naoya Ando); Some Remarks on Noncommutative Instantons (Nikolay A Ivanov); Almost CR Structure on the Twistor Space of a Quaternionic CR Manifold (Hiroyuki Kamada and Shin Nayatani); Five Dimensional Lie Groups Which are Almost Contact B-Metric Manifolds with Three Natural Connections (Miroslava Ivanova and Hristo Manev); On Hyperelliptic Minimal Surfaces with Even Genus (Norio Ejiri and Toshihiro Shoda); Laplacians of Kahler Graphs (Yaermaimaiti Tuerxunmaimaiti (Yarmamat Tursun)); Hopf Fibration and Cartan Imbedding of Type AI (Hideya Hashimoto and Kazuhiro Suzuki); On Totally Umbilical and Screen Totally Umbilical Radical Transversal Lightlike Hypersurfaces of Kahler-Norden Manifolds (Galia Nakova); Complex Statistical Manifolds and Complex Affine Immersions (Hiroshi Matsuzoe); A Method of Determining the SO(7)-Invariants for Curves in Im O by Their G2-Invariants (Misa Ohashi); Magnetic Jacobi Fields for Surface Magnetic Fields (Qingsong Shi); A Geometric Study on Laplace Transformed Curves (Milen J Hristov); Vector-Valued Laplace Transformation Applied to Rational Bezier Curves (Milen J Hristov);
£106.20
World Scientific Publishing Co Pte Ltd Differential Geometry Of Curves And Surfaces
Book Synopsis'In a class populated by students who already have some exposure to the concept of a manifold, the presence of chapter 3 in this text may make for an unusual and interesting course. The primary function of this book will be as a text for a more conventional course in the classical theory of curves and surfaces.'MAA ReviewsThis engrossing volume on curve and surface theories is the result of many years of experience the authors have had with teaching the most essential aspects of this subject. The first half of the text is suitable for a university-level course, without the need for referencing other texts, as it is completely self-contained. More advanced material in the second half of the book, including appendices, also serves more experienced students well.Furthermore, this text is also suitable for a seminar for graduate students, and for self-study. It is written in a robust style that gives the student the opportunity to continue his study at a higher level beyond what a course would usually offer. Further material is included, for example, closed curves, enveloping curves, curves of constant width, the fundamental theorem of surface theory, constant mean curvature surfaces, and existence of curvature line coordinates.Surface theory from the viewpoint of manifolds theory is explained, and encompasses higher level material that is useful for the more advanced student. This includes, but is not limited to, indices of umbilics, properties of cycloids, existence of conformal coordinates, and characterizing conditions for singularities.In summary, this textbook succeeds in elucidating detailed explanations of fundamental material, where the most essential basic notions stand out clearly, but does not shy away from the more advanced topics needed for research in this field. It provides a large collection of mathematically rich supporting topics. Thus, it is an ideal first textbook in this field.
£69.35
EPB Publishers Pte Ltd Riemannian Geometry, Fibre Bundles, Kaluza-klein
Book Synopsis
£63.65
EPB Publishers Pte Ltd Riemannian Geometry, Fibre Bundles, Kaluza-klein
Book SynopsisThis book discusses the geometrical aspects of Kaluza-Klein theories. The ten chapters cover topics from the differential and Riemannian manifolds to the reduction of Einstein-Yang-Mills action. It would definitely prove interesting reading to physicists and mathematicians, theoretical and experimental.
£103.50
Springer International Publishing AG Selected Works I
Book SynopsisThis is a two-volume collection presenting the selected works of Herbert Busemann, one of the leading geometers of the twentieth century and one of the main founders of metric geometry, convexity theory and convexity in metric spaces. Busemann also did substantial work (probably the most important) on Hilbert’s Problem IV. These collected works include Busemann’s most important published articles on these topics. Volume I of the collection features Busemann’s papers on the foundations of geodesic spaces and on the metric geometry of Finsler spaces. Volume II includes Busemann’s papers on convexity and integral geometry, on Hilbert’s Problem IV, and other papers on miscellaneous subjects. Each volume offers biographical documents and introductory essays on Busemann’s work, documents from his correspondence and introductory essays written by leading specialists on Busemann’s work. They are a valuable resource for researchers in synthetic and metric geometry, convexity theory and the foundations of geometry. Table of ContentsPreface.- Introduction to Volume I.- List of publications of Herbert Busemann.- Acknowledgements.- Essays.- A. Papadpoulos: Herbert Busemann (1905-1994).- A. Papadopoulos and M. Troyanov: On three early papers by Herbert Busemann on the foundations of geometry.- M. Troyanov: On Pasch's Axiom and Desargues' Theorem in Busemann's work.- V. N. Berestovskiy: Busemann's results, ideas, questions on locally compact homogeneous geodesic spaces.- A. Papadopoulos and S. Yamada: Busemann's problems on G-spaces.- Busemann's metric theory of timelike spaces.- A. Papadopoulos: Chronogeometry.- W. M. Boothby: Review of Busemann's book The geometry of Geodesics.- F. A. Ficken: Review of Busemann's book Metric Methods in Finsler Spaces and in the Foundations of Geometry.- Busemann's papers on the foundations of geodesic spaces and on the metric geometry of Finsler spaces.
£999.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Some Nonlinear Problems in Riemannian Geometry
Book SynopsisThis book deals with such important subjects as variational methods, the continuity method, parabolic equations on fiber bundles, ideas concerning points of concentration, blowing-up technique, geometric and topological methods. It explores important geometric problems that are of interest to many mathematicians and scientists but have only recently been partially solved.Table of Contents1 Riemannian Geometry.- 2 Sobolev Spaces.- 3 Background Material.- 4 Complementary Material.- 5 The Yamabe Problem.- 6 Prescribed Scalar Curvature.- 7 Einstein—Kähler Metrics.- 8 Monge—Ampère Equations.- 9 The Ricci Curvature.- 10 Harmonic Maps.- Bibliography*.- Notation.
£999.99
Springer Fachmedien Wiesbaden Lineare Algebra für die Natur- und
Book SynopsisDieses Lehrbuch behandelt die zentralen Themen der Linearen Algebra einschließlich ihrer Anwendungen. Neben einer systematischen Einführung der Rechenoperationen mit Vektoren und Matrizen werden entsprechende Rechengesetze angegeben, und es wird erklärt, warum diese gelten. Zahlreiche sehr ausführlich vorgerechnete Beispiele machen das Lehrbuch zu einer wertvollen Basis für das Selbststudium oder zur Vorbereitung auf Prüfungen. Viele dieser Beispiele geben außerdem einen Einblick, welche Problemstellungen mittels der Vektor- und Matrizenrechnung behandelt werden können. Neben allgemeinen Lösungsstrategien für lineare Gleichungssysteme werden Lösungsalgorithmen diskutiert, welche auf spezifische Anwendungsgebiete abgestimmt sind – z. B. Algorithmen zur Lösung von tridiagonalen Gleichungssystemen, von Gleichungssystemen mit einer symmetrischen, positiv definiten Matrix und von Gleichungssystemen, die in der Ausgleichungsrechnung auftreten. Für eine ganze Reihe von Problemen wie der Lösung linearer Gleichungssysteme, der Berechnung von Determinanten und der Berechnung der Inversen einer Matrix werden verschiedene Algorithmen vorgestellt. Bei der Nutzung dieser unterschiedlichen Algorithmen zeigt sich, dass manche davon eine sehr hohe Rechenzeit erfordern, während man mit anderen das Rechenergebnis schon nach einer sehr geringen Rechenzeit erhält. Um einschätzen zu können, welche der Algorithmen wann bevorzugt eingesetzt werden sollten, wird für viele Algorithmen eine Analyse des Aufwandes an Rechenoperationen durchgeführt. Der Inhalt Vektoren – Matrizen – Rechnen mit Vektoren und Matrizen – allgemeine Lösungsalgorithmen für lineare Gleichungssysteme – Lösungsalgorithmen für spezielle Gleichungssysteme Die Zielgruppen Studierende der Natur- und IngenieurwissenschaftenTable of ContentsVektoren.- Matrizen und lineare Gleichungssysteme.- Index.- Literaturverzeichnis.
£999.99
World Scientific Publishing Co Pte Ltd Introduction To The Geometrical Analysis Of
Book SynopsisThis book provides the reader with a gentle path through the multifaceted theory of vector fields, starting from the definitions and the basic properties of vector fields and flows, and ending with some of their countless applications, in the framework of what is nowadays called Geometrical Analysis. Once the background material is established, the applications mainly deal with the following meaningful settings:
£135.00
World Scientific Publishing Co Pte Ltd Biharmonic Submanifolds And Biharmonic Maps In Riemannian Geometry
Book SynopsisThe book aims to present a comprehensive survey on biharmonic submanifolds and maps from the viewpoint of Riemannian geometry. It provides some basic knowledge and tools used in the study of the subject as well as an overall picture of the development of the subject with most up-to-date important results.Biharmonic submanifolds are submanifolds whose isometric immersions are biharmonic maps, thus biharmonic submanifolds include minimal submanifolds as a subclass. Biharmonic submanifolds also appeared in the study of finite type submanifolds in Euclidean spaces.Biharmonic maps are maps between Riemannian manifolds that are critical points of the bienergy. They are generalizations of harmonic maps and biharmonic functions which have many important applications and interesting links to many areas of mathematics and theoretical physics.Since 2000, biharmonic submanifolds and maps have become a vibrant research field with a growing number of researchers around the world, with many interesting results have been obtained.This book containing basic knowledge, tools for some fundamental problems and a comprehensive survey on the study of biharmonic submanifolds and maps will be greatly beneficial for graduate students and beginning researchers who want to study the subject, as well as researchers who have already been working in the field.
£148.50
Springer International Publishing AG An Introduction to Riemannian Geometry: With Applications to Mechanics and Relativity
Book SynopsisUnlike many other texts on differential geometry, this textbook also offers interesting applications to geometric mechanics and general relativity.The first part is a concise and self-contained introduction to the basics of manifolds, differential forms, metrics and curvature. The second part studies applications to mechanics and relativity including the proofs of the Hawking and Penrose singularity theorems. It can be independently used for one-semester courses in either of these subjects.The main ideas are illustrated and further developed by numerous examples and over 300 exercises. Detailed solutions are provided for many of these exercises, making An Introduction to Riemannian Geometry ideal for self-study.Trade ReviewFrom the book reviews:“The aim of the textbook is twofold. First, it is a concise and self-contained quick introduction to the basics of differential geometry, including differential forms, followed by the main ideas of Riemannian geometry. Second, the last two chapters are devoted to some interesting applications to geometric mechanics and relativity. … the book is well written and also very readable. I warmly recommend it to specialists in mathematics, physics and engineering, especially to Ph.D. students.” (Miroslaw Doupovec, zbMATH 1306.53001, 2015)Table of ContentsDifferentiable Manifolds.- Differential Forms.- Riemannian Manifolds.- Curvature.- Geometric Mechanics.- Relativity.
£999.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Differential Geometric Methods in Mathematical Physics: Proceedings of the International Conference Held at the Technical University of Clausthal, Germany, July 1978
Book SynopsisOn a geometric quantization scheme generalizing those of Kostant-Souriau and Czyz.- Further applications of geometric quantization.- General vector field representations of local Heisenberg systems.- Aspects of relativistic quantum mechanics on phase space.- On the confinement of magnetic poles.- SU(3) and SU(4) as spectrum-generating groups.- The phase space for the Yang-Mills equations.- Instantons in nonlinear ?-models, gauge theories and general relativity.- Gauge-theoretical foundation of color geometrodynamics.- Non-associative algebras and exceptional gauge groups.- Atiyah-Singer index theorem and quantum field theory.- Topological concepts in phase transition theory.- Life without T2.- Affine model of internal degrees of freedom in a non-euclidean space.- Jet bundles and weyl geometry.- Line fields and Lorentz manifolds.- The manifold of embeddings of a closed manifold.- The manifold of embeddings of a non-compact manifold.Table of ContentsOn a geometric quantization scheme generalizing those of Kostant-Souriau and Czyz.- Further applications of geometric quantization.- General vector field representations of local Heisenberg systems.- Aspects of relativistic quantum mechanics on phase space.- On the confinement of magnetic poles.- SU(3) and SU(4) as spectrum-generating groups.- The phase space for the Yang-Mills equations.- Instantons in nonlinear ?-models, gauge theories and general relativity.- Gauge-theoretical foundation of color geometrodynamics.- Non-associative algebras and exceptional gauge groups.- Atiyah-Singer index theorem and quantum field theory.- Topological concepts in phase transition theory.- Life without T2.- Affine model of internal degrees of freedom in a non-euclidean space.- Jet bundles and weyl geometry.- Line fields and Lorentz manifolds.- The manifold of embeddings of a closed manifold.- The manifold of embeddings of a non-compact manifold.
£999.99
Springer Verlag, Singapore Geometric Inequalities and Applications
£999.99
Independently Published Smooth Manifolds
£999.99
Birkhauser Verlag AG A Visual Introduction to Differential Forms and
Book SynopsisThis book explains and helps readers to develop geometric intuition as it relates to differential forms. It includes over 250 figures to aid understanding and enable readers to visualize the concepts being discussed. The author gradually builds up to the basic ideas and concepts so that definitions, when made, do not appear out of nowhere, and both the importance and role that theorems play is evident as or before they are presented. With a clear writing style and easy-to- understand motivations for each topic, this book is primarily aimed at second- or third-year undergraduate math and physics students with a basic knowledge of vector calculus and linear algebra.Trade Review “The reviewer recommends young mathematics and physics majors to open the book and to keep it on their bookshelves. Indeed, the reviewer even envies young students who can study differential forms with such a fascinating book.” (Hirokazu Nishimura, zbMath 1419.58001, 2019)Table of Contents
£53.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Optimal Transport: Old and New
Book SynopsisAt the close of the 1980s, the independent contributions of Yann Brenier, Mike Cullen and John Mather launched a revolution in the venerable field of optimal transport founded by G. Monge in the 18th century, which has made breathtaking forays into various other domains of mathematics ever since. The author presents a broad overview of this area, supplying complete and self-contained proofs of all the fundamental results of the theory of optimal transport at the appropriate level of generality. Thus, the book encompasses the broad spectrum ranging from basic theory to the most recent research results. PhD students or researchers can read the entire book without any prior knowledge of the field. A comprehensive bibliography with notes that extensively discuss the existing literature underlines the book’s value as a most welcome reference text on this subject. Trade ReviewFrom the reviews:"The book is aimed to old and new problems of optimal transport. … This meticulous work is based on very large bibliography … that is converted into a very valuable monograph that presents many statements and theorems written specifically for this approach, complete and self-contained proofs of the most important results, and extensive bibliographical notes." (Mihail Voicu, Zentralblatt MATH, Vol. 1156, 2009)“This book wins the challenge to give a new and broad perspective on the multifacet topic of the optimal mass transport. … Besides extensive and accurate references therein the reader will find comments on related questions barely touched upon in the main text as well as lively presentations on how ideas and results have developed. This book should prove useful both to the expert and to the beginner looking for a reference text on the subject.” (Dario Cordero Erausquin, Mathematical Reviews, Issue 2010 f)“The book is an in-depth, modern, clear exposition of the advanced theory of optimal transport, and it tries to put together in a unified way almost all the recent developments of the theory. … the book is extremely well written and very pleasant to read. … I strongly recommend this excellent book to every researcher or graduate student in the field of optimal transport. … of interest to many mathematicians in different areas, who are simply interested in having an overview of the subject.” (Alessio Figalli, Bulletin of the American Mathematical Society, Vol. 47 (4), February, 2010)Table of ContentsCouplings and changes of variables.- Three examples of coupling techniques.- The founding fathers of optimal transport.- Qualitative description of optimal transport.- Basic properties.- Cyclical monotonicity and Kantorovich duality.- The Wasserstein distances.- Displacement interpolation.- The Monge—Mather shortening principle.- Solution of the Monge problem I: global approach.- Solution of the Monge problem II: Local approach.- The Jacobian equation.- Smoothness.- Qualitative picture.- Optimal transport and Riemannian geometry.- Ricci curvature.- Otto calculus.- Displacement convexity I.- Displacement convexity II.- Volume control.- Density control and local regularity.- Infinitesimal displacement convexity.- Isoperimetric-type inequalities.- Concentration inequalities.- Gradient flows I.- Gradient flows II: Qualitative properties.- Gradient flows III: Functional inequalities.- Synthetic treatment of Ricci curvature.- Analytic and synthetic points of view.- Convergence of metric-measure spaces.- Stability of optimal transport.- Weak Ricci curvature bounds I: Definition and Stability.- Weak Ricci curvature bounds II: Geometric and analytic properties.
£999.99
World Scientific Publishing Co Pte Ltd Differential Geometry Of Curves And Surfaces
Book Synopsis'In a class populated by students who already have some exposure to the concept of a manifold, the presence of chapter 3 in this text may make for an unusual and interesting course. The primary function of this book will be as a text for a more conventional course in the classical theory of curves and surfaces.'MAA ReviewsThis engrossing volume on curve and surface theories is the result of many years of experience the authors have had with teaching the most essential aspects of this subject. The first half of the text is suitable for a university-level course, without the need for referencing other texts, as it is completely self-contained. More advanced material in the second half of the book, including appendices, also serves more experienced students well.Furthermore, this text is also suitable for a seminar for graduate students, and for self-study. It is written in a robust style that gives the student the opportunity to continue his study at a higher level beyond what a course would usually offer. Further material is included, for example, closed curves, enveloping curves, curves of constant width, the fundamental theorem of surface theory, constant mean curvature surfaces, and existence of curvature line coordinates.Surface theory from the viewpoint of manifolds theory is explained, and encompasses higher level material that is useful for the more advanced student. This includes, but is not limited to, indices of umbilics, properties of cycloids, existence of conformal coordinates, and characterizing conditions for singularities.In summary, this textbook succeeds in elucidating detailed explanations of fundamental material, where the most essential basic notions stand out clearly, but does not shy away from the more advanced topics needed for research in this field. It provides a large collection of mathematically rich supporting topics. Thus, it is an ideal first textbook in this field.
£39.90
Mathematical Society of Japan Algebraic Geometry In East Asia -- Hanoi 2005
Book SynopsisThis volume is the outcome of the conference “Algebraic Geometry in East Asia. II” which was held at the Conference Hall (Hanoi, Vietnam) during October 10 - October 14, 2005. It collects two survey articles and eight research articles contributed by the invited lecturers. Topics touched upon in this volume include: Zariski pairs, rational homogeneous manifolds, Kummer surfaces, singularity theory, Cremona groups, algebraic curves, dual varieties, Castelnuovo-Weil lattices and so on. The reader can not only find the current status of a variety of research topics but also enjoy the art of the subjects by leading algebraic geometers.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets except North AmericaTable of ContentsA survey on Zariski pairs by E. A. Bartolo, J. I. Cogolludo, and H. Tokunaga Towards a categorical construction of Lie algebras by K. Saito Elliptic parameters and defining equations for elliptic fibrations on a Kummer surface by M. Kuwata and T. Shioda Characterization of the rational homogeneous space associated to a long simple root by its variety of minimal rational tangents by J. Hong and J.-M. Hwang Maximal divisorial sets in arc spaces by S. Ishii Two non-conjugate embeddings of $S_3\times \mathbb{Z}_2$ into the Cremona group II by V. A. Iskovskikh On the Castelnuovo-Severi inequality for a double covering by C. Keem and A. Ohbuchi Poincare polynomial of a class of signed complete graphic arrangements by G. Jiang, J. Yu, and J. Zhang Singularities of dual varieties in characteristic 2 by I. Shimada On the Castelnuovo-Weil lattices, I by V. Nguyen-Khac and T. Shioda.
£41.80
Mathematical Society of Japan Finsler Geometry, Sapporo 2005 -- In Memory Of
Book SynopsisThe volume contains surveys and original articles based on the talks given at the 40-th Finsler Symposium on Finsler Geometry held in the period September 9-10, 2005 at Hokkaido Tokai University, Sapporo, Japan. The Symposium's purpose was not only a meeting of the Finsler geometers from Japan and abroad, but also to commemorate the memory of the late Professor Makoto Matsumoto. The papers included in this volume contain fundamental topics of modern Riemann-Finsler geometry, interesting not only for specialists in Finsler geometry, but for researchers in Riemannian geometry or other fields of differential geometry and its applications also.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets except North AmericaTable of ContentsPart I. Professor Makoto Matsumoto: Photos of Makoto Matsumoto Matsumoto's legacy. The life and work of Professor Makoto Matsumoto by H. Shimada and S. V. Sabau Part II. Hunting Unicorns and Other Topics of Global Finsler Geometry: On two curvature-driven problems in Riemann-Finsler geometry by D. Bao Curvature properties of $(\alpha, \beta)$-metrics by S. Bacso, X. Cheng, and Z. Shen A connectedness principle in positively curved Finsler manifolds by I. R. Peter Riemann-Finsler surfaces by S. V. Sabau and H. Shimada Finsler geometry in the tangent bundle by L. Tamassy Part III. Finslerian Inspired Differential Geometry: Perturbations of constant connection Wagner spaces by P. L. Antonelli and S. F. Rutz Path geometries and almost Grassmann structures by M. Crampin and D. J. Saunders Ehresmann connections, metrics and good metric derivatives by R. L. Lovas, J. Pek, and J. Szilasi Dynamical systems of the Lagrangian and Hamiltonian mechanical systems by R. Miron Part IV. Complex Finsler Geometry: The Chern-Finsler connection and Finsler-Kahler manifolds by T. Aikou A survey of complex Finsler geometry by P.-M. Wong.
£56.05
World Scientific Publishing Co Pte Ltd Differential Geometry For Physicists
Book SynopsisThis book is divided into fourteen chapters, with 18 appendices as introduction to prerequisite topological and algebraic knowledge, etc. The first seven chapters focus on local analysis. This part can be used as a fundamental textbook for graduate students of theoretical physics. Chapters 8-10 discuss geometry on fibre bundles, which facilitates further reference for researchers. The last four chapters deal with the Atiyah-Singer index theorem, its generalization and its application, quantum anomaly, cohomology field theory and noncommutative geometry, giving the reader a glimpse of the frontier of current research in theoretical physics.Table of ContentsDifferentiable manifold and differential forms; transformation of manifold, Lie group manifold; affine connection and covariant differentiation; Riemannian manifold; symplectic manifold and contact manifold; complex manifolds; homology of manifolds; homotopy of manifold, fibre bundle, classification of fibre bundles; differential geometry of fibre bundle, Yang-Mills gauge theory; characteristic class; Atiyah-Singer index theorem; index theorem on manifold with boundary and on open infinite manifold; family index theorem, topological properties of quantum gauge theory; noncommutative geometry, quantum group and q-deformation of Chern-characters.
£95.40
World Scientific Publishing Co Pte Ltd Lectures On Chern-weil Theory And Witten
Book SynopsisThis invaluable book is based on the notes of a graduate course on differential geometry which the author gave at the Nankai Institute of Mathematics. It consists of two parts: the first part contains an introduction to the geometric theory of characteristic classes due to Shiing-shen Chern and André Weil, as well as a proof of the Gauss-Bonnet-Chern theorem based on the Mathai-Quillen construction of Thom forms; the second part presents analytic proofs of the Poincaré-Hopf index formula, as well as the Morse inequalities based on deformations introduced by Edward Witten.Table of ContentsChern-Weil theory for characteristic classes; Bott and Duistermaat-Heckman formulas; Gauss-Bonnet-Chern theorem; Poincar -Hopf index formula - an analytic proof; morse inequalities - an analytic proof; Thom-Smale and Witten complexes; Atiyah theorem on Kervaire Semi-characteristic.
£999.99
Walter de Gruyter Differential Geometry
Book Synopsis
£72.00
Springer Fachmedien Wiesbaden Differentialgeometrie von Kurven und Flächen
Book SynopsisEs gibt in der Differentialgeometrie von Kurven und FJachen zwei Betrachtungsweisen. Die eine, die man klassische Differentialgeometrie nennen konnte, entstand zusammen mit den Anfangen der Differential-und Integralrechnung. Grob gesagt studiert die klassische Differentialgeometrie lokale Eigenschaften von Kurven und FHichen. Dabei verstehen wir unter lokalen Eigenschaften solche, die nur vom Verhalten der Kurve oder Flache in der Umgebung eines Punktes abhiingen. Die Methoden, die sich als fUr das Studium solcher Eigenschaften geeignet erwiesen haben, sind die Methoden der Differentialrechnung. Aus diesem Grund sind die in der Differentialgeometrie untersuchten Kurven und Flachen durch Funktionen definiert, die von einer gewissen Differenzierbarkeitsklasse sind. Die andere Betrachtungsweise ist die sogenannte globale Differentialgeometrie. Hierbei untersucht man den EinfluB lokaler Eigenschaften auf das Verhalten der gesamten Kurve oder Flache. Der interessanteste und reprasentativste Teil der klassischen Differentialgeometrie ist wohl die Untersuchung von Flachen. Beim Studium von Flachen treten jedoch in nattirlicher Weise einige 10k ale Eigenschaften von Kurven auf. Deshalb benutzen wir dieses erste Kapi tel, urn kurz auf Kurven einzugehen.Table of Contents1 Kurven.- 1.1 Einleitung.- 1.2 Parametrisierte Kurven.- 1.3 Reguläre Kurven. Bogenlänge.- 1.4 Das Vektorprodukt in ?3.- 1.5 Die lokale Theorie von Kurven, die nach der Bogenlänge parametrisiert sind.- 1.6 Die lokale kanonische Form.- 1.7 Globale Eigenschaften ebener Kurven.- 2 Reguläre Flächen.- 2.1 Einleitung.- 2.2 Reguläre Flächen. Urbilder regulärer Werte.- 2.3 Parameterwechsel. Differenzierbare Funktionen auf Flächen.- 2.4 Die Tangentialebene. Das Differential einer Abbildung.- 2.5 Die erste Fundamentalform. Flächeninhalt.- 2.6 Orientierung von Flächen.- 2.7 Eine Charakterisierung kompakter orientierbarer Flächen.- 2.8 Eine geometrische Definition des Flächeninhalts.- 3 Die Geometrie der Gauß-Abbildung.- 3.1 Einleitung.- 3.2 Die Definition der Gauß-Abbildung und ihre fundamentalen Eigenschaften.- 3.3 Die Gauß-Abbildung in lokalen Koordinaten.- 3.4 Vektorfelder.- 3.5 Regelflächen und Minimalflächen.- 4 Die innere Geometrie von Flächen.- 4.1 Einleitung.- 4.2 Isometrie. Konforme Abbildungen.- 4.3 Der Satz von Gauß und die Verträglichkeitsbedingungen.- 4.4 Parallelverschiebung. Geodätische.- 4.5 Der Satz von Gauß-Bonnet und seine Anwendungen.- 4.6 Die Exponentialabbildung. Geodätische Polarkoordinaten.- 4.7 Weitere Eigenschaften von Geodätischen. Konvexe Umgebungen.- Anhang: Beweise der Fundamentalsätze der lokalen Kurven-und Flächentheorie.- Hinweise und Lösungen.- Kommentiertes Literaturverzeichnis.- Namen-und Sachwortverzeichnis.
£999.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Dynamical Systems VII: Integrable Systems
Book SynopsisA collection of five surveys on dynamical systems, indispensable for graduate students and researchers in mathematics and theoretical physics. Written in the modern language of differential geometry, the book covers all the new differential geometric and Lie-algebraic methods currently used in the theory of integrable systems.Table of ContentsContents: Nonholonomic Dynamical Systems, Geometry of Distributions and Variational Problems by A.M. Vershik, V.Ya. Gershkovich.- Integrable Systems and Infinite Dimensional Lie Algebras by M.A. Olshanetsky, M.A. Perelomov.- Group-Theoretical Methods in the Theory of Finite-Dimensional Integrable Systems by A.G. Reyman, M.A. Semenov-Tian-Shansky.- Quantization of Open Toda Lattices by M.A. Semenov-Tian-Shansky.- Geometric and Algebraic Mechanisms of the Integrability of Hamiltonian Systems on Homogeneous Spaces and Lie Algebras by V.V. Trofimov, A.T. Fomenko.
£999.99
Springer Verlag Curves and Surfaces
Book SynopsisThe book provides an introduction to Differential Geometry of Curves and Surfaces. The theory of curves starts with a discussion of possible definitions of the concept of curve, proving in particular the classification of 1-dimensional manifolds. We then present the classical local theory of parametrized plane and space curves (curves in n-dimensional space are discussed in the complementary material): curvature, torsion, Frenet’s formulas and the fundamental theorem of the local theory of curves. Then, after a self-contained presentation of degree theory for continuous self-maps of the circumference, we study the global theory of plane curves, introducing winding and rotation numbers, and proving the Jordan curve theorem for curves of class C2, and Hopf theorem on the rotation number of closed simple curves. The local theory of surfaces begins with a comparison of the concept of parametrized (i.e., immersed) surface with the concept of regular (i.e., embedded) surface. We then develop the basic differential geometry of surfaces in R3: definitions, examples, differentiable maps and functions, tangent vectors (presented both as vectors tangent to curves in the surface and as derivations on germs of differentiable functions; we shall consistently use both approaches in the whole book) and orientation. Next we study the several notions of curvature on a surface, stressing both the geometrical meaning of the objects introduced and the algebraic/analytical methods needed to study them via the Gauss map, up to the proof of Gauss’ Teorema Egregium. Then we introduce vector fields on a surface (flow, first integrals, integral curves) and geodesics (definition, basic properties, geodesic curvature, and, in the complementary material, a full proof of minimizing properties of geodesics and of the Hopf-Rinow theorem for surfaces). Then we shall present a proof of the celebrated Gauss-Bonnet theorem, both in its local and in its global form, using basic properties (fully proved in the complementary material) of triangulations of surfaces. As an application, we shall prove the Poincaré-Hopf theorem on zeroes of vector fields. Finally, the last chapter will be devoted to several important results on the global theory of surfaces, like for instance the characterization of surfaces with constant Gaussian curvature, and the orientability of compact surfaces in R3.Trade ReviewFrom the reviews:“The authors’ goal in writing this book is to present the theory of curves and surfaces from the viewpoint of contemporary mathematics. … New concepts and new definitions are fully motivated, and illustrated by numerous examples. … the book is beautifully written, very well organized, and most of all it may serve as both a less advanced text and a more advanced text for readers interested in the theory of curves and surfaces.” (Andrew Bucki, Mathematical Reviews, June, 2013)“It is dedicated to the study of curves and surfaces both from a local and global viewpoint. It is written and organised in such a way that it can be used by a large scope of students, not only for beginning, intermediate or advanced undergraduate courses in mathematics or physics, but also for engineering or computer science students. … the book can be useful for post-graduate students, too. The book is well written and includes many examples and figures.” (Raúl Oset Sinha, Zentralblatt MATH, Vol. 1238, 2012)
£999.99
Birkhauser Verlag AG Geometric properties of non-compact CR manifolds
Book SynopsisThe book deals with some questions related to the boundary problem in complex geometry and CR geometry. After a brief introduction summarizing the main results on the extension of CR functions, it is shown in chapters 2 and 3 that, employing the classical Harvey-Lawson theorem and under suitable conditions, the boundary problem for non-compact maximally complex real submanifolds of Cn, n=3 is solvable. In chapter 4, the regularity of Levi flat hypersurfaces Cn (n=3) with assigned boundaries is studied in the graph case, in relation to the existence theorem proved by Dolbeault, Tomassini and Zaitsev. Finally, in the last two chapters the structure properties of non-compact Levi-flat submanifolds of Cn are discussed; in particular, using the theory of the analytic multifunctions, a Liouville theorem for Levi flat submanifolds of Cn is proved.
£999.99
Springer Verlag, Singapore Nevanlinna Theory
Book SynopsisThis book deals with the classical theory of Nevanlinna on the value distribution of meromorphic functions of one complex variable, based on minimum prerequisites for complex manifolds. The theory was extended to several variables by S. Kobayashi, T. Ochiai, J. Carleson, and P. Griffiths in the early 1970s. K. Kodaira took up this subject in his course at The University of Tokyo in 1973 and gave an introductory account of this development in the context of his final paper, contained in this book. The first three chapters are devoted to holomorphic mappings from C to complex manifolds. In the fourth chapter, holomorphic mappings between higher dimensional manifolds are covered. The book is a valuable treatise on the Nevanlinna theory, of special interests to those who want to understand Kodaira's unique approach to basic questions on complex manifolds.Table of ContentsPreface1. Nevanlinna Theory of One Variable (1)1.1 metrics of compact Rimann surfaces1.2 integral formula1.3 holomorphic maps over compact Riemann surfaces whose genus are greater than 21.4 holomorphic maps over Riemann sphreres1.5 Defect relation2. Schwarz--Kobayashi's Lemma2.1 Schwarz--Kobayashi's Lemma2.2 holomorphic maps over algebraic varieties (general type)2.3 hyperbolic measures3. Nevanlinna Theory of One Variable (2)3.1 holomorphic maps over Riemann shpres3.2 the first main theorem3.3 the second main theorem4. Nevanlinna Theory of Several Variables4.1 Biebelbach's example4.2 the first main theorem4.3 the second main theorem4.4 defect relation4.5 applicationsReferences
£999.99
Springer Verlag, Singapore Contact Geometry of Slant Submanifolds
Book SynopsisThis book contains an up-to-date survey and self-contained chapters on contact slant submanifolds and geometry, authored by internationally renowned researchers. The notion of slant submanifolds was introduced by Prof. B.Y. Chen in 1990, and A. Lotta extended this notion in the framework of contact geometry in 1996. Numerous differential geometers have since obtained interesting results on contact slant submanifolds. The book gathers a wide range of topics such as warped product semi-slant submanifolds, slant submersions, semi-slant ξ┴ -, hemi-slant ξ┴ -Riemannian submersions, quasi hemi-slant submanifolds, slant submanifolds of metric f-manifolds, slant lightlike submanifolds, geometric inequalities for slant submanifolds, 3-slant submanifolds, and semi-slant submanifolds of almost paracontact manifolds. The book also includes interesting results on slant curves and magnetic curves, where the latter represents trajectories moving on a Riemannian manifold under the action of magnetic field. It presents detailed information on the most recent advances in the area, making it of much value to scientists, educators and graduate students.Table of ContentsGeneral Properties of Slant Submanifolds in Contact Metric Manifolds.- Curvature Inequalities for Slant Submanifolds in Pointwise Kenmotsu Space Forms.- Some Basic Inequalities on Slant submanifolds in Space forms.- Geometry of Warped Product Semi-Slant Submanifolds in Almost Contact Metric Manifolds.- Slant and Semi Slant Submanifolds of Almost Contact and Paracontact Metric Manifolds.- The Slant Submanifolds in the Setting of Metric f-manifolds.- Slant, Semi-Slant and Pointwise Slant Submanifolds of 3-Structure Manifolds.- Slant Submanifolds of Conformal Sasakian Space Forms.- Slant Curves and Magnetic Curves.- Contact Slant Geometry of Submersions and Pointwise Slant and Semi-Slant Warped Product Submanifolds.
£999.99
Springer Verlag, Singapore Complex Geometry of Slant Submanifolds
Book SynopsisThis book contains an up-to-date survey and self-contained chapters on complex slant submanifolds and geometry, authored by internationally renowned researchers. The book discusses a wide range of topics, including slant surfaces, slant submersions, nearly Kaehler, locally conformal Kaehler, and quaternion Kaehler manifolds. It provides several classification results of minimal slant surfaces, quasi-minimal slant surfaces, slant surfaces with parallel mean curvature vector, pseudo-umbilical slant surfaces, and biharmonic and quasi biharmonic slant surfaces in Lorentzian complex space forms. Furthermore, this book includes new results on slant submanifolds of para-Hermitian manifolds. This book also includes recent results on slant lightlike submanifolds of indefinite Hermitian manifolds, which are of extensive use in general theory of relativity and potential applications in radiation and electromagnetic fields. Various open problems and conjectures on slant surfaces in complex space forms are also included in the book. It presents detailed information on the most recent advances in the area, making it valuable for scientists, educators and graduate students.Trade Review“As a global view, one must mention that many of the presented results in the above contributions are given with their complete proofs; this fact increases the value of the book and makes it excellent scientific material for the researchers in the field. Besides the high level and the valuable contents of the book, one must remark that the topic is of high interest for the specialists in differential geometry.” (Adela-Gabriela Mihai, zbMATH 1511.53002, 2023)Table of ContentsAn Overview of Recent Developments of Slant Submanifolds.- Slant Surfaces in Complex Space Forms.- Slant Geometry of Warped products in Kaehler and Nearly Kaehler Manifolds.- Slant Geometry of Riemannian Submersions from Almost Hermitian Manifolds.- Slant Submanifolds of the nearly Kaehler 6-sphere.- Slant submanifolds of para Hermitian manifolds.- Hemi-slant and Semi-slant Submanifolds in locally conformal Kaehler Manifolds.- Slant Submanifolds and Their Warped Product in Locally Product Riemannian Manifolds.- Slant Submanifolds of Quaternion Kaehler and Hyper-Kaehler Manifolds.- Geometry of Pointwise Slant Immersions in Almost Hermitian Manifolds.
£999.99
Springer Verlag, Singapore Einstein Constraints and Ricci Flow: A
Book SynopsisThis book contains a self-consistent treatment of a geometric averaging technique, induced by the Ricci flow, that allows comparing a given (generalized) Einstein initial data set with another distinct Einstein initial data set, both supported on a given closed n-dimensional manifold. This is a case study where two vibrant areas of research in geometric analysis, Ricci flow and Einstein constraints theory, interact in a quite remarkable way. The interaction is of great relevance for applications in relativistic cosmology, allowing a mathematically rigorous approach to the initial data set averaging problem, at least when data sets are given on a closed space-like hypersurface. The book does not assume an a priori knowledge of Ricci flow theory, and considerable space is left for introducing the necessary techniques. These introductory parts gently evolve to a detailed discussion of the more advanced results concerning a Fourier-mode expansion and a sophisticated heat kernel representation of the Ricci flow, both of which are of independent interest in Ricci flow theory. This work is intended for advanced students in mathematical physics and researchers alike. Table of ContentsIntroduction.- Geometric preliminaries.- Ricci flow background.- Ricci flow conjugation of initial data sets.- Concluding remarks.
£999.99
de Gruyter Weighted Morrey Spaces
Book Synopsis
£116.85
