Transformation Groups in Differential Geometry

Description

Cover Title page Preface I. Automorphisms of G-Structures 1. G-Structures 2. Examples of G-Structures 3. Two Theorems on Differentiable Transformation Groups 4. Automorphisms of Compact Elliptic Structures 5. Prolongations of G-Structures 6. Volume Elements and Symplectic Structures 7. Contact Structures 8. Pseudogroup Structures, G-Structures and Filtered Lie Algebras II. Isometries of Riemannian Manifolds 1. The Group of Isometries of a Riemannian Manifold 2. Infinitesimal Isometries and Infinitesimal Affine Transformations 3. Riemannian Manifolds with Large Group of Isometries 4. Riemannian Manifolds with Little Isometries 5. Fixed Points of Isometries 6. Infinitesimal Isometries and Characteristic Numbers III. Automorphisms of Complex Manifolds 1. The Group of Automorphisms of a Complex Manifold 2. Compact Complex Manifolds with Finite Automorphism Groups 3. Holomorphic Vector Fields and Holomorphic 1-Forms 4. Holomorphic Vector Fields on Kähler Manifolds 5. Compact Einstein-Kähler Manifolds 6. Compact Kähler Manifolds with Constant Scalar Curvature 7. Conformal Changes of the Laplacian 8. Compact Kähler Manifolds with Nonpositive First Chern CIass 9. Projectively Induced Holomorphic Transformations 10. Zeros of Infinitesimal Isometries 11. Zeros of Holomorphic Vector Fields 12. Holomorphic Vector Fields and Characteristic Numbers IV. Affine, Conformal and Projective Transformations 1. The Group of Affine Transformations of an Affinely Connected Manifold 2. Affine Transformations of Riemannian Manifolds 3. Cartan Connections 4. Projective and Conformal Connections 5. Frames of Second Order 6. Projective and Conformal Structures 7. Projective and Conformal Equivalences Appendices 1. Reductions of 1-Forms and Closed 2-Forms 2. Some Integral Formulas 3. Laplacians in Local Coordinates 4. A Remark on d'd"-Cohomology Bibliography Index