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.

arXiv commentTo appear in Kyoto Journal of Mathematics

References in corpus (6)

• Invariant metrics and Laplacians on Siegel-Jacobi space
• Some remarks on homogeneous Kähler manifolds
• The Simanca metric admits a regular quantization
• Holomorphic isometries into homogeneous bounded domains
• On holomorphic isometries into blow-ups of ${\mathbb{C}}^n$
• Rigidity properties of holomorphic isometries into homogeneous Kähler manifolds