Lectures on the Automorphism Groups of Kobayashi-Hyperbolic Manifolds

Name: Lectures on the Automorphism Groups of Kobayashi-Hyperbolic Manifolds
Price: 37.77 USD
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ISBN: 9783540691518

ISBN-10: 3540691510

ISBN-13: 9783540691518

Edition: 2007

Authors: Alexander Isaev

List price: $49.95

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Description:

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.

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.




Introduction



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>


References


Index