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Riemannian Geometry and Geometric Analysis
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Catalogue Information
Field name
Details
Dewey Class
516.36
Title
Riemannian Geometry and Geometric Analysis ([EBook]) / by Jürgen Jost.
Author
Jost, Jürgen , 1956-
Other name(s)
SpringerLink (Online service)
Edition statement
Second Edition.
Publication
Berlin, Heidelberg : Springer , 1998.
Physical Details
XIII, 458 pages : online resource.
Series
Universitext
0172-5939
ISBN
9783662223857
Summary Note
From the reviews: "This book provides a very readable introduction to Riemannian geometry and geometric analysis. The author focuses on using analytic methods in the study of some fundamental theorems in Riemannian geometry,e.g., the Hodge theorem, the Rauch comparison theorem, the Lyusternik and Fet theorem and the existence of harmonic mappings. With the vast development of the mathematical subject of geometric analysis, the present textbook is most welcome. It is a good introduction to Riemannian geometry. The book is made more interesting by the perspectives in various sections, where the author mentions the history and development of the material and provides the reader with references." Math. Reviews. The second edition contains a new chapter on variational problems from quantum field theory, in particular the Seiberg-Witten and Ginzburg-Landau functionals. These topics are carefully and systematically developed, and the new edition contains a thorough treatment of the relevant background material, namely spin geometry and Dirac operators. The new material is based on a course "Geometry and Physics" at the University of Leipzig that was attented by graduate students, postdocs and researchers from other areas of mathematics. Much of the material is included here for the first time in a textbook, and the book will lead the reader to some of the hottest topics of contemporary mathematical research.:
Contents note
1. Foundational Material -- 2. De Rham Cohomology and Harmonic Differential Forms -- 3. Parallel Transport, Connections, and Covariant Derivatives -- 4. Geodesics and Jacobi Fields -- A Short Survey on Curvature and Topology -- 5. Morse Theory and Closed Geodesics -- 6. Symmetric Spaces and Kähler Manifolds -- 7. The Palais-Smale Condition and Closed Geodesics -- 8. Harmonic Maps -- 9. Variational Problems from Quantum Field Theory -- Appendix A: Linear Elliptic Partial Differential Equation -- A.1 Sobolev Spaces -- A.2 Existence and Regularity Theory for Solutions of Linear Elliptic Equations -- Appendix B: Fundamental Groups and Covering Spaces.
System details note
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site
http://dx.doi.org/10.1007/978-3-662-22385-7
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Subject References:
Differential Geometry
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Mathematics
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Authors:
Jost, Jürgen 1956-
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Jost, Jürgen, 1956-
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Corporate Authors:
SpringerLink (Online service)
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Series:
Universitext
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Classification:
516.36
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