Lectures on the Automorphism Groups of Kobayashi-Hyperbolic Manifolds

• Main Author: Isaev, Alexander (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2007.
• Series: Lecture Notes in Mathematics, 1902
• Subjects: Mathematics.; Functions of complex variables.; Several Complex Variables and Analytic Spaces.
• Physical Description: VIII, 144 p. online resource.
• ISBN: 9783540691532
• ISSN: 0075-8434 ;

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.