Riemannian Geometry / by Peter Petersen.

Format:

Book

Author/Creator:

Petersen, Peter, 1962- Author.

Series:

Graduate Texts in Mathematics, 0072-5285 ; 171

Language:

English

Subjects (All):

Geometry, Differential.

Differential Geometry.

Local Subjects:

Differential Geometry.

Physical Description:

1 online resource (XVIII, 499 p. 50 illus., 1 illus. in color.)

Edition:

3rd ed. 2016.

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2016.

Language Note:

English

Summary:

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. From reviews of the first edition: "The book can be highly recommended to all mathematicians who want to get a more profound idea about the most interesting achievements in Riemannian geometry. It is one of the few comprehensive sources of this type." ―Bernd Wegner, ZbMATH.

Contents:

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.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Description based on publisher supplied metadata and other sources.

ISBN:

3-319-26654-3

OCLC:

945365475