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Lectures on the Automorphism Groups of Kobayashi-Hyperbolic Manifolds

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ISBN-10: 3540691510

ISBN-13: 9783540691518

Edition: 2007

Authors: Alexander Isaev

List price: $49.95
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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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Book details

List price: $49.95
Copyright year: 2007
Publisher: Springer Berlin / Heidelberg
Publication date: 2/9/2007
Binding: Paperback
Pages: 144
Size: 6.10" wide x 9.25" long x 0.50" tall
Weight: 0.990
Language: English

Alexander Isaev is a senior lecturer in mathematics at The Australian National University, Canberra. His mathematical background is the area of several complex variables. After completing a PhD degree in 1990 at the Moscow State University, he taught at the University of Illinois (Urbana-Champaign) and at Chalmers University of Technology, GAteborg, Sweden. One is his current interests is in applying mathematics to biology.

The Automorphism Group as a Lie Group
The Classification Problem
A Lacuna in Automorphism Group Dimensions
Main Tools
The Homogeneous Case
Homogeneity for d(M) > n<sup>2</sup>
Classification of Homogeneous Manifolds
The Case d(M) = n<sup>2</sup>
Main Result
Initial Classification of Orbits
Real Hypersurface Orbits
Proof of Theorem 3.1
The Case d(M) = n<sup>2</sup> - 1, n &geq; 3
Main Result
Initial Classification of Orbits
Non-Existence of Real Hypersurface Orbits
Proof of Theorem 4.1
The Case of (2,3)-Manifolds
Examples of (2,3)-Manifolds
Strongly Pseudoconvex Orbits
Levi-Flat Orbits
Codimension 2 Orbits
Proper Actions
General Remarks
The Case G &simeq; U<sub>n</sub>
The Case G &simeq; SU<sub>n</sub>