Description
Book SynopsisPresents an introduction to differential geometry. This book then introduces Lie groups and Lie algebras. It concludes with the classification of symmetric spaces by means of the Killing-Cartan classification of simple Lie algebras over $\mathbf{C}$ and Cartan's classification of simple Lie algebras over $\mathbf{R}$.
Trade ReviewThis book has been famous for many years and used by several generations of readers. It is important that the book has again become available for a general audience." -
European Mathematical Society Newsletter"One of the most important and excellent textbooks and a reference work about contemporary differential geometry …" -
Zentralblatt MATH"Important improvements in the new edition of S. Helgason's book will turn it into a desk book for many following generations." -
Mathematica BohemicaFrom reviews for the First Edition:
"A great book … a necessary item in any mathematical library." - S. S. Chern, University of California
"Written with unmatched lucidity, systematically, carefully, beautifully." - S. Bochner, Princeton University
"Helgason's monograph is a beautifully done piece of work and should be extremely useful for several years to come, both in teaching and in research." - D. Spencer, Princeton University
"A brilliant book: rigorous, tightly organized, and covering a vast amount of good mathematics." - Barrett O'Neill, University of California
"Renders a great service in permitting the non-specialist, with a minimum knowledge of differential geometry and Lie groups, an initiation to the theory of symmetrical spaces." - H. Cartan, Secretariat Mathématique, Paris
"The mathematical community has long been in need of a book on symmetric spaces. S. Helgason has admirably satisfied this need with his book,
Differential Geometry and Symmetric Spaces. It is a remarkably well-written book … a masterpiece of concise, lucid mathematical exposition … it might be used as a textbook for “how to write mathematics”."- Louis Auslander
"[The author] will earn the gratitude of many generations of mathematicians for this skillful, tasteful, and highly efficient presentation. It will surely become a classic." - G. D. Mostow, Yale University
Table of Contents
- Preface to original edition
- Preface to the 2001 printing
- Suggestions to the reader
- Sequel to the present volume
- Groups and geometric analysis contents
- Geometric analysis on symmetric spaces contents
- Elementary differential geometry
- Lie groups and Lie algebras
- Structure of semisimple Lie algebras
- Symmetric spaces
- Decomposition of symmetric spaces
- Symmetric spaces of the noncompact type
- Symmetric spaces of the compact type
- Hermitian symmetric spaces
- Structure of semisimple Lie groups
- The classification of simple Lie algebras and of symmetric spaces
- Solutions to exercises
- Some details
- Bibliography
- List of notational conventions
- Symbols frequently used
- Index
- Reviews for the first edition
