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题名/责任者:

Riemannian geometry / Peter Petersen.

版本说明:

Third edition.

出版发行项:

Cham ; New York, NY : Springer International Publishing AG, c2016

ISBN:

9783319266527 :

ISBN:

3319266527

载体形态项:

xviii, 499 pages : illustrations ; 24 cm

丛编说明:

Graduate texts in mathematics ; 171.

丛编统一题名:

Graduate texts in mathematics.

个人责任者:

Petersen, Peter, 1962- author.

论题主题:

Geometry, Riemannian.

中图法分类号:

O186.12

书目附注:

Includes bibliographical references (pages 491-494) and index.

内容附注:

Preface -- 1. Riemannian Metrics.-2. Derivatives -- 3. Curvature -- 4. Examples -- 5. Geodesics and Distance -- 6. Sectional Curvature Comparison I.- 7. Ricci Curvature Comparison.- 8. Killing Fields -- 9. The Bochner Technique -- 10. Symmetric Spaces and Holonomy -- 11. Convergence -- 12. Sectional Curvature Comparison II -- Bibliography -- Index.

内容附注:

Riemannian Metrics -- Derivatives -- Curvature -- Examples -- Geodesics and Distance -- Sectional Curvature Comparison I -- Ricci Curvature Comparison -- Killing Fields -- The Bochner Technique -- Symmetric Spaces and Holonomy -- Convergence -- Sectional Curvature Comparison II.

摘要附注:

"Intended for a one year course, this text serves as a single source, introducing readers to the important techniques and theorems, while also containing enough background on advanced topics to appeal to those students wishing to specialize in Riemannian geometry. This is one of the few Works to combine both the geometric parts of Riemannian geometry and the analytic aspects of the theory. The book will appeal to a readership that have a basic knowledge of standard manifold theory, including tensors, forms, and Lie groups. Important revisions to the third edition include: a substantial addition of unique and enriching exercises scattered throughout the text; inclusion of an increased number of coordinate calculations of connection and curvature; addition of general formulas for curvature on Lie Groups and submersions; integration of variational calculus into the text allowing for an early treatment of the Sphere theorem using a proof by Berger; incorporation of several recent results about manifolds with positive curvature; presentation of a new simplifying approach to the Bochner technique for tensors with application to bound topological quantities with general lower curvature bounds."--Back cover.

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