Description
Hindustan Book Agency A Course in Differential Geometry and Lie Groups 2002 Edition by S. Kumaresan
This book arose out of courses taught by the author. It covers the traditional topics of differential manifolds, tensor fields, Lie groups, integration on manifolds and basic differential and Riemannian geometry. The author emphasizes geometric concepts, giving the reader a working knowledge of the topic. Motivations are given, exercises are included, and illuminating nontrivial examples are discussed._x000D__x000D_Important features include the following: _x000D__x000D__x000D__x000D_Geometric and conceptual treatment of differential calculus with a wealth of nontrivial examples. _x000D_A thorough discussion of the much-used result on the existence, uniqueness, and smooth dependence of solutions of ODEs. _x000D_Careful introduction of the concept of tangent spaces to a manifold. _x000D_Early and simultaneous treatment of Lie groups and related concepts. _x000D_A motivated and highly geometric proof of the Frobenius theorem. _x000D_A constant reconciliation with the classical treatment and the modern approach. _x000D_Simple proofs of the hairy-ball theorem and Brouwer's fixed point theorem. _x000D_Construction of manifolds of constant curvature a la Chern. _x000D__x000D__x000D__x000D_This text would be suitable for use as a graduate-level introduction to basic differential and Riemannian geometry._x000D_ Table of Contents :- _x000D_
Contents: 1. Diferential Calculus 2. Manifolds and Lie Groups 3. Tensor Analysis 4. Integration 5. Riemannian Geometry. Bibliography. List of Symbols.Index._x000D_