Riemannian geometry and geometric analysis
 Author/Creator
 Jost, Jürgen, 1956
 Language
 English.
 Edition
 6th ed.
 Imprint
 Heidelberg ; New York : Springer, c2011.
 Physical description
 xiii, 611 p. : ill. ; 24 cm.
 Series
 Universitext.
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Available online

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QA649 .J67 2011

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QA649 .J67 2011
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Contents/Summary
 Bibliography
 Includes bibliographical references (p. 587604) and index.
 Contents

 1. Riemannian Manifolds. 2. Lie Groups and Vector Bundles. 3. The Laplace Operator and Harmonic Differential Forms. 4. Connections and Curvature. 5. Geodesics and Jacobi Fields. 6. Symmetric Spaces and Kahler Manifolds. 7. Morse Theory and Floer Homology. 8. Harmonic Maps between Riemannian Manifolds. 9. Harmonic Maps from Riemann Surfaces. 10. Variational Problems from Quantum Field Theory. A. Linear Elliptic Partial Differential Equations. A.1 Sobolev Spaces. A.2 Linear Elliptic Equations. A.3 Linear Parabolic Equations. B. Fundamental Groups and Covering Spaces. Bibliography. Index.
 (source: Nielsen Book Data)
 Publisher's Summary
 This established reference work continues to lead its readers to some of the hottest topics of contemporary mathematical research. The previous edition already introduced and explained the ideas of the parabolic methods that had found a spectacular success in the work of Perelman at the examples of closed geodesics and harmonic forms. It also discussed further examples of geometric variational problems from quantum field theory, another source of profound new ideas and methods in geometry. The 6th edition includes a systematic treatment of eigenvalues of Riemannian manifolds and several other additions. Also, the entire material has been reorganized in order to improve the coherence of the book. From the reviews: "This book provides a very readable introduction to Riemannian geometry and geometric analysis...With the vast development of the mathematical subject of geometric analysis, the present textbook is most welcome." Mathematical Reviews "...the material ...is selfcontained. Each chapter ends with a set of exercises. Most of the paragraphs have a section 'Perspectives', written with the aim to place the material in a broader context and explain further results and directions." Zentralblatt MATH.
(source: Nielsen Book Data)  Supplemental links

Contributor biographical information
Publisher description
Table of contents only
Contributor biographical information
Publisher description
Table of contents only
Subjects
Bibliographic information
 Publication date
 2011
 Responsibility
 Jürgen Jost.
 Series
 Universitext
 ISBN
 9783642212970
 3642212972