On homogeneous holomorphic conformal structures

2024/05/04 by Belraouti, Mehdi, Deffaf, Mohamed, Raffed, Yazid +1 · 2 citations
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2405.02527

Abstract

We study compact complex manifolds M admitting a conformal holomorphic Riemannian structure invariant under the action of a complex semi-simple Lie group G. We prove that if the group G acts transitively and essentially, then M is conformally flat.

Cited by

• Pseudo-Conformal actions of semisimple Lie groups
• Semi-Riemannian metrics on compact simple Lie Groups

Related

• Pseudo-Conformal actions of semisimple Lie groups
• Pseudo-Conformal Actions of the Möbius Group
• Transitive conformal holonomy groups
• Semi-simple Lie groups acting conformally on compact Lorentz manifolds
• Nonnegatively curved fixed point homogeneous manifolds in low dimensions