Transformation Groups in Differential Geometry (Classics in Mathematics)

TRANSFORMATION GROUPS IN DIFFERENTIAL GEOMETRY......Page 1
Title Page......Page 2
Copyright Page......Page 3
Inner Title Page......Page 4
Inner Copyright Page......Page 5
Preface......Page 6
Contents......Page 8
1. G-Structures......Page 10
2. Examples of G-Structures......Page 14
3. Two Theorems on Differentiable Transformation Groups......Page 22
4. Automorphisms of Compact Elliptic Structures......Page 25
5. Prolongations of G-Structures......Page 28
6. Volume Elements and Symplectic Structures......Page 32
7. Contact Structures......Page 37
8. Pseudogroup Structures, G-Structures and Filtered Lie Algebras......Page 42
1. The Group of Isometries of a Riemannian Manifold......Page 48
2. Infinitesimal Isometrics and Infinitesimal Affine Transformations......Page 51
3. Riemannian Manifolds with Large Group of Isometries......Page 55
4. Riemannian Manifolds with Little Isometries......Page 64
5. Fixed Points of Isometries......Page 68
6. Infinitesimal Isometries and Characteristic Numbers......Page 76
1. The Group of Automorphisms of a Complex Manifold......Page 86
2. Compact Complex Manifolds with Finite Automorphism Groups......Page 91
3. Holomorphic Vector Fields and Holomorphic 1-Forms......Page 99
4. Holomorphic Vector Fields on Kähler Manifolds......Page 101
5. Compact Einstein–Kähler Manifolds......Page 104
6. Compact Kähler Manifolds with Constant Scalar Curvature......Page 106
7. Conformal Changes of the Laplacian......Page 109
8. Compact Kähler Manifolds with Nonpositive First Chern Class......Page 112
9. Projectively Induced Holomorphic Transformations......Page 115
10. Zeros of Infinitesimal Isometries......Page 121
11. Zeros of Holomorphic Vector Fields......Page 124
12. Holomorphic Vector Fields and Characteristic Numbers......Page 128
1. The Group of Affine Transformations of an Affinely Connected Manifold......Page 131
2. Affine Transformations of Riemannian Manifolds......Page 134
3. Cartan Connections......Page 136
4. Projective and Conformal Connections......Page 140
5. Frames of Second Order......Page 148
6. Projective and Conformal Structures......Page 150
7. Projective and Conformal Equivalences......Page 154
1. Reductions of 1-Forms and Closed 2-Forms......Page 159
2. Some Integral Formulas......Page 163
3. Laplacians in Local Coordinates......Page 166
4. A Remark on d'd"-Cohomology......Page 168
Bibliography......Page 169
Index......Page 190
Back Cover......Page 192