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The index theorem and the heat equation method

Author: Yanlin Yu
Publisher: Singapore ; River Edge, NJ : World Scientific, ©2001.
Series: Nankai tracts in mathematics, v. 2.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:

This volume provides a self-contained represenation of the local version of the Atiyah-Singer index theorem. It contains proofs of the Hodge theorem, the local index theorems for the Dirac operator  Read more...

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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Yanlin Yu
ISBN: 9810246102 9789810246105
OCLC Number: 47994927
Description: xix, 287 pages ; 23 cm.
Contents: Ch. 1. Preliminaries in Riemannian Geometry. 1.1. Basic Notions of Riemannian Geometry. 1.2. Computations by using Orthonormal Moving Frame. 1.3. Differential Forms and Orthonormal Moving Frame Method. 1.4. Classical Geometric Operators. 1.5. Normal Coordinates. 1.6. Computations on Sphere. 1.7. Connections on Vector Bundles and Principal Bundles. 1.8. General Tensor Calculus --
Ch. 2. Schrodinger and Heat Operators. 2.1. Fundamental Solution and Levi Iteration. 2.2. Existence of Fundamental Solution. 2.3. Cauchy Problem of Heat Equation. 2.4. Hodge Theorem. 2.5. Applications of Hodge Theorem. 2.6. Index Problem --
Ch. 3. MP Parametrix and Applications. 3.1. MP Parametrix. 3.2. Existence of Initial Solutions.
Series Title: Nankai tracts in mathematics, v. 2.
Responsibility: Yanlin Yu.
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