Extensions of extremal Kähler submanifolds of complex projective spaces

Abstract

In this paper we showed that every connected extremal Kähler submanifold of a complex projetive space has a natural extension which is a complete Kähler manifold and admits a holomorphic isometric immersion into the same ambient space. We also give an application to study extremal Kähler hypersurfaces of complex projective spaces.

arXiv comment19 pages