Lectures on the Automorphism Groups of Kobayashi-Hyperbolic Manifolds

Alexander Isaev (auth.)3540691510, 9783540691518, 9783540691532

Kobayashi-hyperbolic manifolds are an object of active research in complex geometry. In this monograph the author presents a coherent exposition of recent results on complete characterization of Kobayashi-hyperbolic manifolds with high-dimensional groups of holomorphic automorphisms. These classification results can be viewed as complex-geometric analogues of those known for Riemannian manifolds with high-dimensional isotropy groups, that were extensively studied in the 1950s-70s. The common feature of the Kobayashi-hyperbolic and Riemannian cases is the properness of the actions of the holomorphic automorphism group and the isometry group on respective manifolds.

Table of contents :
Front Matter….Pages I-VIII
Introduction….Pages 1-22
The Homogeneous Case….Pages 23-28
The Case d ( M ) = n 2 ….Pages 29-50
The Case d ( M ) = n 2 – 1, n ≥ 3….Pages 51-60
The Case of (2,3)-Manifolds….Pages 61-119
Proper Actions….Pages 121-130
Back Matter….Pages 131-143