A course in differential geometry and lie groups
By: Kumaresan, S.
Material type:
BookSeries: Texts and readings in mathematics. / edited by V. S. Borkar; v.22.Publisher: New Delhi Hindustan Book Agency 2002Description: xi, 295p.ISBN: 8185931291.Subject(s): Mathematics | Mathematics, GeneralDDC classification: 510 | K96c Summary: 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. Important features include the following: Geometric and conceptual treatment of differential calculus with a wealth of nontrivial examples. A thorough discussion of the much-used result on the existence, uniqueness, and smooth dependence of solutions of ODEs. Careful introduction of the concept of tangent spaces to a manifold. Early and simultaneous treatment of Lie groups and related concepts. A motivated and highly geometric proof of the Frobenius theorem. A constant reconciliation with the classical treatment and the modern approach. Simple proofs of the hairy-ball theorem and Brouwer's fixed point theorem. Construction of manifolds of constant curvature a la Chern. This text would be suitable for use as a graduate-level introduction to basic differential and Riemannian geometry.
| Item type | Current location | Collection | Call number | Status | Date due | Barcode | Item holds |
|---|---|---|---|---|---|---|---|
Books
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PK Kelkar Library, IIT Kanpur | General Stacks | 510 K96c (Browse shelf) | Available | GB1568 |
Browsing PK Kelkar Library, IIT Kanpur Shelves , Collection code: General Stacks Close shelf browser
| 510 K842m2 MATHEMATICAL HANDBOOK FOR SCIENTISTS AND ENGINEERS | 510 K953kE BRIEF COURSE OF HIGHER MATHEMATICS | 510 K957hE HANDBOOK OF MATHEMATICS | 510 K96c A course in differential geometry and lie groups | 510 K99m MATHEMATICS FOR THE CHEMIST | 510 L111e ELEMENTARY MATHEMATICAL ANALYSIS | 510 L132m MATHEMATICS FOR GENERAL EDUCATION |
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. Important features include the following: Geometric and conceptual treatment of differential calculus with a wealth of nontrivial examples. A thorough discussion of the much-used result on the existence, uniqueness, and smooth dependence of solutions of ODEs. Careful introduction of the concept of tangent spaces to a manifold. Early and simultaneous treatment of Lie groups and related concepts. A motivated and highly geometric proof of the Frobenius theorem. A constant reconciliation with the classical treatment and the modern approach. Simple proofs of the hairy-ball theorem and Brouwer's fixed point theorem. Construction of manifolds of constant curvature a la Chern. This text would be suitable for use as a graduate-level introduction to basic differential and Riemannian geometry.
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