On homogeneous holomorphic conformal structures

TL;DR

This paper investigates compact complex manifolds with conformal holomorphic Riemannian structures under complex semi-simple Lie group actions, proving that transitive and essential actions imply conformal flatness.

Contribution

It establishes that such manifolds are conformally flat when acted upon transitively and essentially by a complex semi-simple Lie group.

Findings

Manifolds are conformally flat under specified conditions

Transitive and essential group actions imply conformal flatness

Provides conditions for conformal structures on complex manifolds

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.