Riemannian Geometry

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This comprehensive introduction to Riemannian Geometry offers a detailed and engaging account of the topic, plus numerous exercises and examples. It combines both the geometric parts of Riemannian geometry and the analytic aspects of the theory, and reviews the latest research.
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Introduction.- Riemannian Metrics.- Curvature.- Examples.- Hypersurfaces.- Geodesics and Distance.- Sectional Curvature Comparison I.- The Bochner Technique.- Symmetric Spaces and Holonomy.- Ricci Curvature Comparison.- Convergence.- Sectional Curvature Comparison II.- Appendix A: De Rham Cohomology.- Bibliography.- Index.
This volume introduces techniques and theorems of Riemannian geometry, and opens the way to advanced topics. The text combines the geometric parts of Riemannian geometry with analytic aspects of the theory, and reviews recent research. The updated second edition includes a new coordinate-free formula that is easily remembered (the Koszul formula in disguise); an expanded number of coordinate calculations of connection and curvature; general fomulas for curvature on Lie Groups and submersions; variational calculus integrated into the text, allowing for an early treatment of the Sphere theorem using a forgotten proof by Berger; recent results regarding manifolds with positive curvature.

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Autor: Peter Petersen
ISBN-13 :: 9781441921239
ISBN: 1441921230
Erscheinungsjahr: 23.11.2010
Verlag: Springer New York
Gewicht: 637g
Seiten: 424
Sprache: Englisch
Auflage 10002, Softcover reprint of hardcover 2nd ed. 2006
Sonstiges: Taschenbuch, 235x155x22 mm
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