Riemannian Manifolds
An Introduction to Curvature
(Sprache: Englisch)
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...
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Klappentext zu „Riemannian Manifolds “
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.
Inhaltsverzeichnis zu „Riemannian Manifolds “
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.
Bibliographische Angaben
- Autor: John M. Lee
- 1997, 1997, 226 Seiten, Maße: 16 x 24,1 cm, Gebunden, Englisch
- Verlag: Springer, New York
- ISBN-10: 038798271X
- ISBN-13: 9780387982717
- Erscheinungsdatum: 05.09.1997
Sprache:
Englisch
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