Riemannian Geometry

by ;
Format: Hardcover
Pub. Date: 1992-02-01
Publisher(s): SPRINGER VERLAG
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Summary

This text has been adopted at:University of Pennsylvania, PhiladelphiaUniversity of Connecticut, StorrsDuke University, Durham, NCCalifornia Institute of Technology, PasadenaUniversity of Washington, SeattleSwarthmore College, Swarthmore, PAUniversity of Chicago, ILUniversity of Michigan, Ann Arbor"In the reviewer's opinion, this is a superb book which makes learning a real pleasure."¿ Revue Romaine de Mathematiques Pures et Appliquees"This main-stream presentation of differential geometry serves well for a course on Riemannian geometry, and it is complemented by many annotated exercises."¿ Monatshefte F. Mathematik"This is one of the best (if even not just the best) book for those who want to get a good, smooth and quick, but yet thorough introduction to modern Riemannian geometry."¿ Publicationes MathematicaeContents: Differential Manifolds * Riemannian Metrics * Affine Connections; Riemannian Connections * Geodesics; Convex Neighborhoods * Curvature * Jacobi Fields * Isometric Immersions * Complete Manifolds; Hopf-Rinow and Hadamard Theorems * Spaces of Constant Curvature * Variations of Energy * The Rauch Comparison Theorem * The Morse Index Theorem * The Fundamental Group of Manifolds of Negative Curvature * The Sphere Theorem * IndexSeries: Mathematics: Theory and Applications

Table of Contents

Preface to the 1st edition
Preface to the 2nd edition
Preface to the English edition
How to use this book
Differentiable Manifolds
Riemannian Metrics
Affine Connections
Riemannian Connections
Geodesics
Convex Neighborhoods
Curvature
Jacobi Fields
Isometric Immersions
Complete Manifolds
Hopf-Rinow and Hadamard Theorems
Spaces of Constant Curvature
Variations of Energy
The Rauch Comparison Theorem
The Morse Index Theorem
The Fundamental Group of Manifolds of Negative Curvature
The Sphere Theorem
References
Index
Table of Contents provided by Publisher. All Rights Reserved.

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