English

Nearly K\"ahler submanifolds of a space form

Differential Geometry 2014-11-18 v2

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.

Keywords

Cite

@article{arxiv.1405.2721,
  title  = {Nearly K\"ahler submanifolds of a space form},
  author = {Nikrooz Heidari and Abbas Heydari},
  journal= {arXiv preprint arXiv:1405.2721},
  year   = {2014}
}