The Laplacian on a Riemannian Manifold 黎曼流形上的拉普拉斯算子伦敦数学会学生文本系列

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736 736 九五品

库存2件

广东广州

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作者Steven Rosenberg

出版社Cambridge University Press

ISBN9780521468312

出版时间1995-04

装帧平装

开本其他

定价736元

货号YB-70522

上书时间2024-03-10

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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.

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The Laplacian on a Riemannian Manifold 黎曼流形上的拉普拉斯算子 伦敦数学会学生文本系列