Download E-books The Laplacian on a Riemannian Manifold: An Introduction to Analysis on Manifolds (London Mathematical Society Student Texts) PDF
By Steven Rosenberg
This article on research on Riemannian manifolds is an intensive advent to themes coated in complicated learn monographs on Atiyah-Singer index concept. the most subject matter is the research of warmth circulation linked to the Laplacians on differential kinds. this gives a unified therapy of Hodge conception and the supersymmetric evidence of the Chern-Gauss-Bonnet theorem. specifically, there's a cautious remedy of the warmth kernel for the Laplacian on services. the writer develops the Atiyah-Singer index theorem and its functions (without whole proofs) through the warmth equation technique. Rosenberg additionally treats zeta capabilities for Laplacians and analytic torsion, and lays out the lately exposed relation among index concept and analytic torsion. The textual content is geared toward scholars who've had a primary direction in differentiable manifolds, and the writer develops the Riemannian geometry used from the start. There are over a hundred routines with tricks.