Nearly Kähler submanifolds of a space form. (English) Zbl 1353.53021
Summary: In this article, we study isometric immersions of nearly Kähler manifolds into a space form (especially Euclidean space) and show that every nearly Kähler submanifold of a space form has an umbilic foliation whose leaves 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.
MSC:
| 53B25 | Local submanifolds |
| 53B35 | Local differential geometry of Hermitian and Kählerian structures |
| 53C55 | Global differential geometry of Hermitian and Kählerian manifolds |
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