Lectures on the geometry of manifolds
Material type:
TextLanguage: English Publication details: Singapore: World Scientific, 2021 Edition: 3rd edDescription: xviii, 682p. PbkISBN: 9780000990334Subject(s): MATHEMATICS | GEOMETRY | POISSON MANIFOLDSDDC classification: 514.7 Summary: The goal of this book is to introduce the reader to some of the main techniques, ideas and concepts frequently used in modern geometry. It starts from scratch and it covers basic topics such as differential and integral calculus on manifolds, connections on vector bundles and their curvatures, basic Riemannian geometry, calculus of variations, DeRham cohomology, integral geometry (tube and Crofton formulas), characteristic classes, elliptic equations on manifolds and Dirac operators. The new edition contains a new chapter on spectral geometry presenting recent results which appear here for the first time in printed form.
| Item type | Current library | Call number | Status | Date due | Barcode |
|---|---|---|---|---|---|
NBHM Books
|
NISER LIBRARY | 514.7 NIC-L (Browse shelf(Opens below)) | Checked out to Anupam Pal Choudhury (SMSF0142) | 03/06/2024 | N366 |
Contents:
1. Manifolds
2. Natural Constructions on Manifolds
3. Calculus on Manifolds
4. Riemannian Geometry
5. Elements of the Calculus of Variations
6. The Fundamental Group and Covering Spaces
7. Cohomology
8. Characteristic Classes
9. Classical Integral Geometry
10. Elliptic Equations on Manifolds
11. Spectral Geometry
12. Dirac Operators
The goal of this book is to introduce the reader to some of the main techniques, ideas and concepts frequently used in modern geometry. It starts from scratch and it covers basic topics such as differential and integral calculus on manifolds, connections on vector bundles and their curvatures, basic Riemannian geometry, calculus of variations, DeRham cohomology, integral geometry (tube and Crofton formulas), characteristic classes, elliptic equations on manifolds and Dirac operators. The new edition contains a new chapter on spectral geometry presenting recent results which appear here for the first time in printed form.
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