The Laplacian on a Riemannian Manifold

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 t...See More