On Hermitian manifolds whose Chern connection is Ambrose-Singer

TL;DR

This paper studies compact Hermitian manifolds with Chern connections that have parallel torsion and curvature, providing structure theorems for this specific class of manifolds.

Contribution

It introduces and characterizes a new class of Hermitian manifolds with Ambrose-Singer Chern connections, establishing their structural properties.

Findings

Structure theorems for such manifolds

Characterization of parallel torsion and curvature

Insights into the geometry of Hermitian manifolds

Abstract

We consider the class of compact Hermitian manifolds whose Chern connection is Ambrose-Singer, namely, it has parallel torsion and curvature. We prove structure theorems for such manifolds.