The Laplacian on a Riemannian Manifold: An Introduction to

The Laplacian on a Riemannian Manifold: An Introduction to Analysis on Manifolds (London Mathematical Society Student Texts)

This text on analysis on Riemannian manifolds is a thorough introduction to topics covered in advanced research monographs on Atiyah-Singer index theory. The main theme is the study of heat flow associated to the Laplacians on differential forms. This provides a unified treatment of Hodge theory and the supersymmetric proof of the Chern-Gauss-Bonnet theorem. In particular, there is a careful treatment of the heat kernel for the Laplacian on functions. The author develops the Atiyah-Singer index theorem and its applications (without complete proofs) via the heat equation method. Rosenberg also treats zeta functions for Laplacians and analytic torsion, and lays out the recently uncovered relation between index theory and analytic torsion. The text is aimed at students who have had a first course in differentiable manifolds, and the author develops the Riemannian geometry used from the beginning. There are over 100 exercises with hints.

Country	USA
Author	Steven Rosenberg
Binding	Paperback
Brand	Brand: Cambridge University Press
EAN	9780521468312
Edition	1
Feature	Used Book in Good Condition
ISBN	0521468310
Label	Cambridge University Press
Manufacturer	Cambridge University Press
NumberOfItems	1
NumberOfPages	188
PublicationDate	1997-01-28
Publisher	Cambridge University Press
Studio	Cambridge University Press
ReleaseDate	0000-00-00

The Laplacian on a Riemannian Manifold: An Introduction to Analysis on Manifolds (London Mathematical Society Student Texts)