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Further Steps Towards Classifying Homogeneous Kobayashi-Hyperbolic Manifolds with High-Dimensional Automorphism Group

  • Alexander IsaevEmail author
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Abstract

We determine all connected homogeneous Kobayashi-hyperbolic manifolds of dimension \(n\ge 4\) whose group of holomorphic automorphisms has dimension either \(n^2-4\), or \(n^2-5\), or \(n^2-6\). This paper continues a series of articles that achieve classifications for automorphism group dimension \(n^2-3\) and greater.

Keywords

Kobayashi-hyperbolic manifolds Homogeneous complex manifolds The group of holomorphic automorphisms 

Mathematics Subject Classification

53C30 53C35 32Q45 32M05 32M10 

Notes

Acknowledgements

Most of the work in this paper was done during the author’s visit to the Steklov Mathematical Institute in Moscow, which the author thanks for its hospitality. We are also grateful to M. Jarnicki and P. Pflug for their help with the editorial procedures required to process this paper for publication.

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Copyright information

© Mathematica Josephina, Inc. 2019

Authors and Affiliations

  1. 1.Mathematical Sciences InstituteAustralian National UniversityCanberraAustralia

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