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Mediterranean Journal of Mathematics

, Volume 13, Issue 5, pp 2525–2537 | Cite as

Nearly Kähler Submanifolds of a Space Form

  • Nikrooz Heidari
  • Abbas Heydari
Article
  • 97 Downloads

Abstract

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 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.

Keywords

Nearly Kähler manifold isometric immersion totally umbilic foliation 

Mathematics Subject Classification

53B35 53C55 

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Copyright information

© Springer Basel 2015

Authors and Affiliations

  1. 1.Department of MathematicsTarbiat Modares UniversityTehranIran

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