Hermitian manifolds: when Chern connection is Ambrose-Singer
This talk is based on joint work with Prof. Lei Ni of UCSD. We will discuss the geometry of a special type of locally homogeneous Hermitian manifolds: those whose Chern connection is Ambrose-Singer, namely with parallel torsion and curvature. We will show that the universal covering spaces of such manifolds are always the product of Hermitian symmetric spaces and complex Lie groups.