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Nearly Kähler Submanifolds of a Space Form

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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.

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Authors and Affiliations

  1. Department of Mathematics, Tarbiat Modares University, 14115-134, Tehran, Iran

    Nikrooz Heidari & Abbas Heydari

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  1. Nikrooz Heidari
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  2. Abbas Heydari
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Correspondence to Abbas Heydari.

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Heidari, N., Heydari, A. Nearly Kähler Submanifolds of a Space Form. Mediterr. J. Math. 13, 2525–2537 (2016). https://doi.org/10.1007/s00009-015-0637-9

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  • DOI: https://doi.org/10.1007/s00009-015-0637-9

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