Riemannian Manifolds: An Introduction to Curvature: 176 - Rilegato

Lee, John M.

Rilegato

ISBN 10: 038798271X ISBN 13: 9780387982717

Casa editrice: Springer Verlag, 1997

Riassunto

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, Bonnets Theorem, and a special case of the Cartan-Ambrose-Hicks Theorem.

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Recensione

"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

Contenuti

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.

Dettagli dell'edizione

• Editore: Springer Verlag
• Data di pubblicazione: 1997
• Lingua: Inglese
• ISBN 10: 038798271X
• ISBN 13: 9780387982717
• Rilegatura: Copertina rigida
• Numero di pagine: 224
• Contatto del produttore: non disponibile
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