Riemannian Geometry and Geometric Analysis [Paperback]

Jurgen Jost (Author), J. Jost (Author)

Book Description

ISBN-10: 3540426272 | ISBN-13: 978-3540426271 | Publication Date: December 6, 2001 | Edition: 03

The second edition featured a new chapter with a systematic development of variational problems from quantum field theory, in particular the Seiberg-Witten and Ginzburg-Landau functionals. This third edition gives a new presentation of Morse theory and Floer homology that emphasises the geometric aspects and integrates it into the context of Riemannian geometry and geometric analysis. It also gives a new presentation of the geometric aspects of harmonic maps: This uses geometric methods from the theory of geometric spaces of nonpositive curvature and, at the same time, sheds light on these, as an excellent example of the integration of deep geometric insights and powerful analytical tools. These new materials are based on a course at the University of Leipzig, entitled Geometry and Physics, attended by graduate students, postdocs and researchers from other areas of mathematics. Much of this material appears for the first time in a textbook.

Editorial Reviews

From the Back Cover

This established reference work continues to lead its readers to some of the hottest topics of contemporary mathematical research.This new edition introduces and explains the ideas of the parabolic methods that have recently found such a spectacular success in the work of Perelman at the examples of closed geodesics and harmonic forms. It also discusses further examples of geometric variational problems from quantum field theory, another source of profound new ideas and methods in geometry. 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. [..] The book is made more interesting by the perspectives in various sections." Mathematical Reviews --This text refers to an alternate Paperback edition.

About the Author

Jürgen Jost is Codirector of the Max Planck Institute for Mathematics in the Sciences in Leipzig, Germany, an Honorary Professor at the Department of Mathematics and Computer Sciences at Leipzig University, and an External Faculty Member of the Santa Fe Institute for the Sciences of Complexity, New Mexico, USA. He is the author of a number of further Springer textbooks including Postmodern Analysis (1997, 2002, 2005), Compact Riemann Surfaces (1997, 2002, 2006), Partial Differential Equations (2002, 2007), Differentialgeometrie und MInimalflächen (1994, 2007, with J. Eschenburg), Dynamical Systems (2005), as well as several research monographs, such as Geometry and Physics (2009), and many publications in scientific journals. --This text refers to an alternate Paperback edition.

Product Details

• Paperback: 545 pages
• Publisher: Springer; 03 edition (December 6, 2001)
• Language: English
• ISBN-10: 3540426272
• ISBN-13: 978-3540426271
• Product Dimensions: 9 x 6.6 x 1.2 inches
• Shipping Weight: 1.8 pounds
• Average Customer Review: 4.5 out of 5 stars  See all reviews (2 customer reviews)
• Amazon Best Sellers Rank: #1,857,808 in Books (See Top 100 in Books)

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10 of 14 people found the following review helpful:

4.0 out of 5 stars maths background for General Relativity and QFT, January 10, 2007

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This review is from: Riemannian Geometry and Geometric Analysis (Universitext) (Paperback)

For theoretical physicists, especially those studying Einstein's Theory of General Relativity, Or if your subject is quantum field theory. Jost's book is good preparation. He offers an in-depth teaching of Riemannian geometry. So ideas like covariant and contravariant derivatives on a manifold take on elegant meaning.

Note that General Relativity does not get an explicit mention. However, a typical physics GR course might often not have time to give a good discussion of the underlying maths. And standard GR texts, like Misner, Thorne and Wheeler or Weinberg, also tend to have very abbreviated explanations of the maths. So Jost's book is useful for those of you inclined to look further.

The length of the book means it's probably too long for a standard 1 term or semester course, if the intent is to entirely cover the book.

9 of 36 people found the following review helpful:

5.0 out of 5 stars Intro to Riemannian Geom. and Geom. Analysis, July 2, 1999

By A Customer

This review is from: Riemannian Geometry, Geometric Analysis (Universitext) (Paperback)

Covers standard material on Reimannian Geometry. In addition: variational problems from QFT. Spin geometry and Dirac operators are explained in detail.