Submanifolds of Kaehlerian manifold with a metric compound structure of rank 2

Abstract

The metric compound structure of rank r is an obstructed structure of an induced structure on a real submanifold in an almost Hermitian manifold. In this paper we deal with a submanifold with metric compound structure of rank 2 in a Kaehlerian manifold and we classify it under some suitable conditions. Namely it is a standard sphere or neither Einstein nor conformally flat.