Riemannian Geometry

by Carmo, Manfredo Perdigao Do; Flaherty, Francis

• ISBN13: 9780817634902
• ISBN10: 0817634908
• Format: Hardcover
• Copyright: 1992-02-01
• Publisher: Birkhauser

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.