Nearly K\"ahler submanifolds of a space form

Abstract

In this article we study isometric immersions of nearly K\"ahler manifolds into a space form (specially Euclidean space) and show that every nearly K\"ahler submanifold of a space form has a totally umbilic foliation whose leafs are 6-dimensional nearly K\"ahler manifolds. Moreover using this foliation we show that there is no non-homogeneous 6-dimensional nearly K\"ahler submanifold of a space form. We prove some results towards a classification of nearly K\"ahler hypersurfaces in standard space forms.