arXiv subjects
Publications and source records attributed to Nikrooz Heidari.
We study the foliation space of complex and invariant (by torsion of intrinsic Hermitian connection) umbilic distribution on an isometric immersion from a nearly Kähler manifold $M$ into the Euclidean space. Under suitable conditions this leaf space is nearly Kähler and $M$ can be decomposed into a product of this leaf space and a 6-dimensional locally homogeneous nearly Kähler manifold.
In this article we study isometric immersions of nearly Kähler manifolds into a space form (specially Euclidean space) and show that every nearly Kähler submanifold of a space form has a totally umbilic foliation whose leafs are 6-dimensional nearly Kähler manifolds. Moreover using this foliation we show that there is no non-homogeneous 6-dimensional nearly Kähler submanifold of a space form. We prove some results towards a classification of nearly Kähler hypersurfaces in standard space forms.