Chern+Ambrose-Singer = Lie

The geometry of connections is the core of gauge theory. For a 
complex manifold endowed with a Hermitian metric, the Chern connection 
is the one compatible with the metric and the holomorphic structure. 
Extending a result of Cartan on symmetric spaces, Ambrose-Singer 
introduced a connection to capture the homogeneity of a Riemannian 
manifold. In this talk I shall discuss a classification result on 
complex manifolds whose Chern connection is Amrose-Singer. In a joint 
work with F. Zheng we proved that the universal cover of such a manifold 
must be products of Hermitian symmetric spaces with complex Lie groups.

https://mathweb.ucsd.edu/~lni/