Description

Book Synopsis

This book provides a tour of the principal areas and methods of modern differential geometry. Beginning at the introductory level with curves in Euclidian space, the sections become more challenging, arriving finally at the advanced topics that form the greatest part of the book: transformation groups, the geometry of differential equations, geometric structures, the equivalence problem, the geometry of elliptic operators.



Table of Contents
1. Introduction: A Metamathematical View of Differential Geometry.- 2. The Geometry of Surfaces.- 3. The Field Approach of Riemann.- 4. The Group Approach of Lie and Klein. The Geometry of Transformation Groups.- 5. The Geometry of Differential Equations.- 6. Geometric Structures.- 7. The Equivalence Problem, Differential Invariants and Pseudogroups.- 8. Global Aspects of Differential Geometry.- Commentary on the References.- References.- Author Index.

Geometry I: Basic Ideas and Concepts of

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    A Hardback by R.V. Gamkrelidze, E. Primrose, D.V. Alekseevskij

    15 in stock


      View other formats and editions of Geometry I: Basic Ideas and Concepts of by R.V. Gamkrelidze

      Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
      Publication Date: 07/11/1991
      ISBN13: 9783540519997, 978-3540519997
      ISBN10: 3540519998
      Also in:
      Mathematics Differential and Riemannian geometry

      Description

      Book Synopsis

      This book provides a tour of the principal areas and methods of modern differential geometry. Beginning at the introductory level with curves in Euclidian space, the sections become more challenging, arriving finally at the advanced topics that form the greatest part of the book: transformation groups, the geometry of differential equations, geometric structures, the equivalence problem, the geometry of elliptic operators.



      Table of Contents
      1. Introduction: A Metamathematical View of Differential Geometry.- 2. The Geometry of Surfaces.- 3. The Field Approach of Riemann.- 4. The Group Approach of Lie and Klein. The Geometry of Transformation Groups.- 5. The Geometry of Differential Equations.- 6. Geometric Structures.- 7. The Equivalence Problem, Differential Invariants and Pseudogroups.- 8. Global Aspects of Differential Geometry.- Commentary on the References.- References.- Author Index.

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