On weak and strict relatives Kähler manifolds

Abstract

We study Kähler manifolds that are (weak) relatives, that is, Kähler manifolds which share a (locally isometric) submanifold. In particular, we prove that if two Kähler manifolds are weak relatives and one of them is projective, then they are relatives. Moreover, we introduce the notion of strict relatives Kähler manifolds and provide several nontrivial examples.

To appear in Kyoto Journal of Mathematics