TY  - BOOK
AU  - Rosenberg,Steven
TI  - The Laplacian on a Riemannian manifold: an introduction to analysis on manifolds 
T2  - London Mathematical Society student texts
SN  - 9780511623783 (ebook)
AV  - QA649 .R68 1997
U1  - 516.3/73 20
PY  - 1997///
CY  - Cambridge
PB  - Cambridge University Press
KW  - Riemannian manifolds
KW  - Laplacian operator
N1  - Title from publisher's bibliographic system (viewed on 05 Oct 2015)
N2  - This text on analysis of 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 Atiyah-Singer index theorem and its applications are developed (without complete proofs) via the heat equation method. Zeta functions for Laplacians and analytic torsion are also treated, and the recently uncovered relation between index theory and analytic torsion is laid out. The text is aimed at students who have had a first course in differentiable manifolds, and the Riemannian geometry used is developed from the beginning. There are over 100 exercises with hints
UR  - https://doi.org/10.1017/CBO9780511623783
ER  -