The Laplacian on a Riemannian Manifold pdf epub mobi txt 电子书下载 2024

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Steven Rosenberg

Cambridge University Press

1997-1-28

188

USD 62.00

Paperback

London Mathematical Society Student Texts

9780521468312

图书标签: 黎曼几何数学几何分析 Mathematics 微分几何7 几何 Riemann_Geometry 机器学习

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发表于2024-11-22

The Laplacian on a Riemannian Manifold epub 下载 mobi 下载 pdf 下载 txt 电子书下载 2024

The Laplacian on a Riemannian Manifold pdf epub mobi txt 电子书下载 2024

图书描述

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.

The Laplacian on a Riemannian Manifold 下载 mobi epub pdf txt 电子书