Riemannian Manifolds

Riemannian Manifolds : An Introduction to Curvature

4.14 (27 ratings by Goodreads)
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Description

This text focuses on developing an intimate acquaintance with the geometric meaning of curvature and thereby introduces and demonstrates all the main technical tools needed for a more advanced course on Riemannian manifolds. It covers proving the four most fundamental theorems relating curvature and topology: the Gauss-Bonnet Theorem, the Cartan-Hadamard Theorem, Bonnet's Theorem, and a special case of the Cartan-Ambrose-Hicks Theorem.
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Product details

  • Paperback | 226 pages
  • 155 x 235 x 11.94mm | 790g
  • New York, NY, United States
  • English
  • 1997 ed.
  • XV, 226 p.
  • 0387983228
  • 9780387983226
  • 513,652

Table of contents

What Is Curvature?.- Review of Tensors, Manifolds, and Vector Bundles.- Definitions and Examples of Riemannian Metrics.- Connections.- Riemannian Geodesics.- Geodesics and Distance.- Curvature.- Riemannian Submanifolds.- The Gauss-Bonnet Theorem.- Jacobi Fields.- Curvature and Topology.
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Review quote

"This book is very well writen, pleasant to read, with many good illustrations. It deals with the core of the subject, nothing more and nothing less. Simply a recommendation for anyone who wants to teach or learn about the Riemannian geometry."
Nieuw Archief voor Wiskunde, September 2000
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Rating details

27 ratings
4.14 out of 5 stars
5 41% (11)
4 37% (10)
3 19% (5)
2 4% (1)
1 0% (0)
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