Page 10 - Curvature and Homology

X CONTENTS
3.4 Infinitesimal transformations .....
3.5 The derivation 0(X) .........
3.6 Lie transformation groups ......
3.7 Conformal transformations ......
3.8 Conformal transformations (continued) .
3.9 Conformally flat manifolds ......
3.10 Afiine collineations .........
3.11 Projective transformatiohs ......
Exercises ...............
Chapter 1V
COMPACT LIE GROUPS .................... 132
4.1 The Grassman algebra of a Lie group ................ 132
4.2 Invariant differential forms .................... 134
4.3 Local geometry of a compact semi-simple Lie group ......... 136
4.4 Harmonic forms on a compact semi-simple Lie group ........ 139
4.5 Curvature and betti numbers of a compact semi-simple Lie group G . . 141
4.6 Determination of the betti numbers of the simple Lie groups ..... 143
Exercises ............................. 145
Chapter V
COMPLEX MANIFOLDS .................... 146
5.1 Complex manifolds ....................... 147
5.2 Almost complex manifolds .................... 150
5.3. Local hermitian geometry .................... 158
5.4 The operators L and A ...................... 168
5.5 Kaehler manifolds ....................... 173
5.6 Topology of a Kaehler manifold .................. 175
5.7 Effective forms on an hermitian manifold .............. 179
5.8 Holomorphic maps . Induced structures ............... 182
5.9 Examples of Kaehler manifolds .................. 184
Exercises ............................. 189
Chapter VI
CURVATURE AND HOMOLOGY OF
KAEHLER MANIFOLDS ................... 197
6.1 Holomorphic curvature ..................... 199
6.2 The effect of positive Ricci curvature ............... 205
6.3 Deviation from constant holomorphic curvature ........... 206
6.4 Kaehler-Einstein spaces ..................... 208
6.5 Holomorphic tensor fields .................... 210
6.6 Complex parallelisable manifolds ................. 213
6.7 Zero curvature ......................... 215
6.8 Compact complex parallelisable manifolds ............. 217
6.9 A topological characterization of compact complex parallelisable manifolds 220
6.10 d"-cohomology ........................ 221
6.1 1 Complex imbedding ...................... 223
6.12 Euler characteristic ....................... 227