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<p>We study compact complex manifolds <i>M</i> admitting a conformal holomorphic Riemannian structure, invariant under the action of a complex semisimple Lie group <i>G</i>. We classify all such manifolds on which <i>G</i> acts transitively and essentially. In particular, we show that they are conformally flat.</p>

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On Homogeneous Holomorphic Conformal Structures

  • 期刊论文

  • 发表日期：

    2025年9月13日

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  • Mohamed Deffaf,
  • Mehdi Belraouti,
  • Yazid Raffed,
  • Abdelghani Zeghib

摘要

We study compact complex manifolds M admitting a conformal holomorphic Riemannian structure, invariant under the action of a complex semisimple Lie group G. We classify all such manifolds on which G acts transitively and essentially. In particular, we show that they are conformally flat.