Lectures on the Automorphism Groups of Kobayashi-Hyperbolic Manifolds [electronic resource] / by Alexander Isaev.
Material type: TextSeries: Lecture Notes in Mathematics ; 1902Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2007Description: VIII, 144 p. online resourceContent type:- text
- computer
- online resource
- 9783540691532
- 515.94 23
- QA331.7
The Homogeneous Case -- The Case d(M) = n2 -- The Case d(M) = n2 - 1, n ? 3 -- The Case of (2,3)-Manifolds -- Proper Actions.
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.
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