Item description for Riemannian Geometry and Geometric Analysis (Universitext) by Jurgen Jost...
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 2nd ed. includes new material on Ginzburg-Landau, Seibert-Witten functionals, spin geometry, Dirac operators.
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Reviews - What do customers think about Riemannian Geometry and Geometric Analysis (Universitext)?
maths background for General Relativity and QFT Jan 11, 2007
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.
Intro to Riemannian Geom. and Geom. Analysis Jul 2, 1999
Covers standard material on Reimannian Geometry. In addition: variational problems from QFT. Spin geometry and Dirac operators are explained in detail.