Lectures on the Automorphism Groups of Kobayashi-Hyperbolic Manifolds

✍ Scribed by Isaev A.

• Book ID: 127448774
• Year: 2007
• Tongue: English
• Weight: 3 MB
• Category: Library

✦ Synopsis

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.