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

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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.

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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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Correspondence to Alexander Isaev.

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Isaev, A. Further Steps Towards Classifying Homogeneous Kobayashi-Hyperbolic Manifolds with High-Dimensional Automorphism Group. J Geom Anal (2019). https://doi.org/10.1007/s12220-019-00227-x

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Keywords

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

Mathematics Subject Classification

  • 53C30
  • 53C35
  • 32Q45
  • 32M05
  • 32M10