Riemannian manifolds : an introduction to curvature
著者
書誌事項
Riemannian manifolds : an introduction to curvature
（Graduate texts in mathematics, 176）
Springer, c1997
- : hardcover
- : pbk
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注記
"With 88 illustrations"
Bibliography: p. [209]-211
Includes index
内容説明・目次
内容説明
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.
目次
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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