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Synopsis
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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About the Author
John M. Lee has been a mathematics professor at the University of Washington in Seattle since 1987. He has written two other popular graduate texts (Introduction to Smooth Manifolds and Introduction to Topological Manifolds), and an undergraduate text (Axiomatic Geometry).
Review
"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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- PublisherSpringer
- Publication date1997
- ISBN 10 038798271X
- ISBN 13 9780387982717
- BindingHardcover
- LanguageEnglish
- Number of pages241
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Riemannian Manifolds: An Introduction to Curvature
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Springer-Verlag New York Inc., 1997
ISBN 10: 038798271X
ISBN 13: 9780387982717
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Riemannian Manifolds : An Introduction to Curvature
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Springer New York, Springer New York, 1997
ISBN 10: 038798271X
ISBN 13: 9780387982717
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Buch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - This book is designed as a textbook for a one-quarter or one-semester graduate course on Riemannian geometry, for students who are familiar with topological and differentiable manifolds. It focuses on developing an intimate acquaintance with the geometric meaning of curvature. In so doing, it introduces and demonstrates the uses of all the main technical tools needed for a careful study of Riemannian manifolds. The author has selected a set of topics that can reasonably be covered in ten to fifteen weeks, instead of making any attempt to provide an encyclopedic treatment of the subject. The book begins with a careful treatment of the machinery of metrics, connections, and geodesics,without which one cannot claim to be doing Riemannian geometry. It then introduces the Riemann curvature tensor, and quickly moves on to submanifold theory in order to give the curvature tensor a concrete quantitative interpretation. From then on, all efforts are bent toward proving the four most fundamental theorems relating curvature and topology: the Gauss-Bonnet theorem (expressing the total curvature of a surface in term so fits topological type), the Cartan-Hadamard theorem (restricting the topology of manifolds of nonpositive curvature), Bonnet's theorem (giving analogous restrictions on manifolds of strictly positive curvature), and a special case of the Cartan-Ambrose-Hicks theorem (characterizing manifolds of constant curvature). Many other results and techniques might reasonably claim a place in an introductory Riemannian geometry course, but could not be included due to time constraints. Seller Inventory # 9780387982717
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Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. 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 mo. Seller Inventory # 5913232
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