Sui Chung Ng, East China Normal U., Shanghai

Holomorphic splitting tangent sequence in Hermitian locally symmetric spaces

Abstract

A complex submanifold is said have its tangent sequence split holomorphically if the pull-back holomorphic tangent bundle from the ambient space is a holomorphic direct sum of its holomorphic tangent bundle and normal bundle.  A theorem of Van de Ven states that a complex submanifold of a projective space is linear if and only if its tangent sequence splits holomorphically. In this talk, we are going to discuss what happens when the ambient space is a compact Hermitian locally symmetric space of non-compact type.