リーマン多様体<br>Riemannian Manifolds : An Introduction to Curvature (Graduate Texts in Mathematics) 〈Vol.176〉

リーマン多様体
Riemannian Manifolds : An Introduction to Curvature (Graduate Texts in Mathematics) 〈Vol.176〉

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  • 製本 Paperback:紙装版/ペーパーバック版/ページ数 252 p./サイズ 88 illus.
  • 言語 ENG
  • 商品コード 9780387983226

基本説明

Designed for a graduate course on Riemannian geometry. Contents: What is curvature; Review of Tensors, Manifolds, and Vector bundles; Definitions and Examples of Riemannian Metrics; Connections; Riemann Geodexics; Geodesics and Distance; and more.

Full 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.

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.