Effective actions of the general indefinite unitary groups on holomorphically separable manifolds

TL;DR

This paper classifies holomorphically separable complex manifolds of a certain dimension that admit an effective action by the indefinite unitary group, and describes their automorphism groups, aiding in their characterization.

Contribution

It provides a complete classification of such manifolds and explicit descriptions of their automorphism groups, extending understanding of group actions on complex manifolds.

Findings

Classified all holomorphically separable manifolds with indefinite unitary group actions.

Provided explicit automorphism group descriptions for these manifolds.

Enabled characterization of manifolds via their automorphism groups.

Abstract

We determine all holomorphically separable complex manifolds of dimension $p+q$ which admits a smooth envelope of holomorphy such that the general indefinite unitary group of size $p+q$ acts effectively by holomorphic transformations. Also we give exact description of the automorphism groups of those complex manifolds. As an application we consider a characterization of those complex manifolds by their automorphism groups.