Riemannian geometry / [Translated by] Francis Flaherty.

By:

Carmo, Manfredo Perdigao

Material type: Text

TextSeries: Mathematics : theory & applicationsPublication details: Berlin Birkhauser 2019. 14th PrintingDescription: 300pages, 24cmISBN:

978-0817634902 (hardbound)

DDC classification:

516.373 CAR

Contents:

Preface -- 1. Riemannian Metrics -- 2. Affine Connections -- Riemannian Connections -- 3. Geodesics -- Convex Neighborhoods -- 4. Curvature -- 5. Jacobi Fields -- 6. Isometric Immersions -- 7. Complete Manifolds -- Hopf-Rinow and Hadamard Theorems -- 8. Spaces of Constant Curvature -- 9. Variations of Energy -- 10. The Rauch Comparison Theorem -- 11. The Morse Index Theorem -- 12. The Fundamental Group of Manifolds of Negative Curvature -- 13. The Sphere Theorem -- References -- Index.

Summary: This is a new and expanded edition of this textbook for first-year graduate students in mathematics and physics, discussing the basic language of Riemannian geometry and presenting some of its most fundamental theorems. It features examples and exercises.

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Holdings
Item type	Current library	Collection	Call number	Status	Date due	Barcode
Books	H.T. Parekh Library	SIAS Collection	516.373 CAR (Browse shelf(Opens below))	Available		K6350

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Previous	516.36 TUL Differential geometry: connections, curvature, and characteristic classes /	516.36002453 SCH Geometrical methods of mathematical physics /	516.362 NIC Lectures on the geometry of manifolds /	516.373 CAR Riemannian geometry /	516.373 KUM Riemannian geometry: concepts, examples and techniques /	516.5 MIL Singular points of complex hypersurfaces /	516.9 KAP Hyperbolic manifolds and discrete groups /	Next

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Preface --
1. Riemannian Metrics --
2. Affine Connections --
Riemannian Connections --
3. Geodesics --
Convex Neighborhoods --
4. Curvature --
5. Jacobi Fields --
6. Isometric Immersions --
7. Complete Manifolds --
Hopf-Rinow and Hadamard Theorems --
8. Spaces of Constant Curvature --
9. Variations of Energy --
10. The Rauch Comparison Theorem --
11. The Morse Index Theorem --
12. The Fundamental Group of Manifolds of Negative Curvature --
13. The Sphere Theorem --
References --
Index.

This is a new and expanded edition of this textbook for first-year graduate students in mathematics and physics, discussing the basic language of Riemannian geometry and presenting some of its most fundamental theorems. It features examples and exercises.

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