微分几何中的变换群

出版时间：2010-9  出版社：世界图书出版公司  作者：小林昭七  页数：182  
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内容概要

　　《微分几何中的变换群》内容包括：Automorphisms of G-Structures、Isometres of Riemannian Manifolds、Automorphisms of Complex Manifolds、Affine， Conformal and Projective Transformations等。

书籍目录

Ⅰ. Automorphisms of G-Structures1. G-Structures2. Examples of G-Structures3. Two Theorems on Differentiable Transformation Groups.4. Automorphisms of Compact Elliptic Structures5. Prolongations of G-Structures6. Volume Elements and Symplectic Structures7. Contact Structures8. Pseudogroup Structures, G-Structures and Filtered Lie AlgebrasⅡ.Isometres of Riemannian Manifolds1. The Group of Isometries of a Riemannian Manifold2. Infinitesimal Isometrics and Infinitesimal Affine Trans formations3. Riemannian Manifolds with Large Group of Isometrics 4. Riemannian Manifolds with Little Isometries5. Fixed Points of Isometrics6. Infinitesimal Isometrics and Characteristic NumbersⅢ. Automorphisms of Complex Manifolds1. The Group of Automorphisms of a Complex Manifold2. Compact Complex Manifolds with Finite Automorphism Groups3. Holomorphic Vector Fields and Holomorphic l-Forms4. Holomorphic Vector Fields on Kahler Manifolds5. Compact Einstein-Kahler Manifolds6. Compact Kahler Manifolds with Constant Scalar Curvature7. Conformal Changes of the Laplacian8. Compact Kahler Manifolds with Nonpositive First Chern Class9. Projectively Induced Holomorphic Transformations.10. Zeros of Infinitesimal Isometries11. Zeros of Holomorphic Vector Fields12. Holomorphic Vector Fields and Characteristic NumbersIV. Affine, Conformal and Projective Transformations1. The Group of Affine Transformations of an Affinely Con nected Manifold2. Affine Transformations of Riemannian Manifolds3. Cartan Connections4. Projective and Conformal Connections5. Frames of Second Order6. Projective and Conformal Structures7. Projective and Conformal EquivalencesAppendices1. Reductions of l-Forms and Closed 2-Forms2. Some Integral Formulas3. Laplacians in Local Coordinates4. A Remark on d'd"-CohomologyBibliographyIndex