Riemannian Geometry and Geometric Analysis (Universitext) | 
 enlarge | Author: Juergen Jost
Publisher: Springer
Category: Book
List Price: $59.95
Buy Used: $54.00
You Save: $5.95 (10%)
Used (2) from $54.00
Rating:  2 reviews
Media: Paperback
Pages: 401
Number Of Items: 1
ISBN: 3540571132
EAN: 9783540571131
Publication Date: September 18, 1997
Availability: Usually ships in 1-2 business days
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Product Description
This textbook introduces techniques from nonlinear analysis at an early stage. Such techniques have recently become an indispensable tool in research in geometry, and they are treated here for the first time in a textbook. Topics include: Differentiable and Riemannian manifolds, metric properties, tensor calculus, vector bundles; the Hodge Theorem for de Rham cohomology; connections and curvature, the Yang-Mills functional; geodesics and Jacobi fields, Rauch comparison theorem and applications; Morse theory (including an introduction to algebraic topology), applications to the existence of closed geodesics; symmetric spaces and Kaehler manifolds; the Palais-Smale condition and closed geodesics; Harmonic maps, minimal surfaces.
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| Customer Reviews:
 Intro to Riemannian Geom. and Geom. Analysis July 2, 1999
6 out of 27 found this review helpful
Covers standard material on Reimannian Geometry. In addition: variational problems from QFT. Spin geometry and Dirac operators are explained in detail.
 maths background for General Relativity and QFT January 11, 2007
W Boudville (Terra, Sol 3)
4 out of 6 found this review helpful
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.
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