What is included with this book?
Preface | p. v |
Introduction and Statement of Results | p. 1 |
Notational Conventions | p. 4 |
Representation Theory | p. 8 |
Affine Structures | p. 10 |
Mixed Structures | p. 13 |
Affine Kähler Structures | p. 16 |
Riemannian Structures | p. 19 |
Weyl Geometry I | p. 21 |
Almost Pseudo-Hermitian Geometry | p. 23 |
The Gray Identity | p. 25 |
Kähler Geometry in the Riemannian Setting I | p. 27 |
Curvature Kähler-Weyl Geometry | p. 28 |
The Covariant Derivative of the Kähler Form I | p. 31 |
Hyper-Hermitian Geometry | p. 34 |
Representation Theory | p. 37 |
Modules for a Group G | p. 37 |
Quadratic Invariants | p. 44 |
Weyl's Theory of Invariants | p. 47 |
Some Orthogonal Modules | p. 53 |
Some Unitary Modules | p. 58 |
Compact Lie Groups | p. 63 |
Connections, Curvature, and Differential Geometry | p. 69 |
Affine Connections | p. 69 |
Equiaffine Connections | p. 72 |
The Levi-Civita Connection | p. 73 |
Complex Geometry | p. 77 |
The Gray Identity | p. 81 |
Kähler Geometry in the Riemannian Setting II | p. 84 |
Real Affine Geometry | p. 89 |
Decomposition of 21 and R as Orthogonal Modules | p. 91 |
The Modules R, S2o, and ¿2 in U | p. 99 |
The Modules Wo6, Wo7, and Wo8 in U | p. 104 |
Decomposition of U as a General Linear Module | p. 106 |
Geometric Readability of Affine Curvature Operators | p. 111 |
Decomposition of U as an Orthogonal Module | p. 124 |
Affine Kähler Geometry | p. 125 |
Affine Kähler Curvature Tensor Quadratic Invariants | p. 125 |
The Ricci Tensor for a Kähler Affine Connection | p. 134 |
Constructing Affine (Para)-Kähler Manifolds | p. 136 |
Affine Kahler Curvature Operators | p. 140 |
Affine Para-Kähler Curvature Operators | p. 149 |
Structure of RU± as a GI± Module | p. 155 |
Riemannian Geometry | p. 173 |
The Riemann Curvature Tensor | p. 174 |
The Weyl Conformal Curvature Tensor | p. 178 |
The Cauchy-Kovalevskaya Theorem | p. 180 |
Geometric Realizations of Riemann Curvature Tensors | p. 181 |
Weyl Geometry II | p. 183 |
Complex Riemannian Geometry | p. 189 |
The Decomposition of R as Modules over U± | p. 190 |
The Submodules of R Arising from the Ricci Tensors | p. 204 |
Para-Hermitian and Pseudo-Hermitian Geometry | p. 210 |
Almost Para-Hermitian and Almost Pseudo-Hermitian Geometry | p. 212 |
Kähler Geometry in the Riemannian Setting III | p. 213 |
Complex Weyl Geometry | |
The Covariant Derivative of the Kähler Form II | p. 221 |
Notational Conventions | p. 235 |
Bibliography | p. 239 |
Index | p. 249 |
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