On some hypersurfaces of the homogeneous nearly Kähler S 3 ×S 3

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On some hypersurfaces of the homogeneous nearly Kähler S 3 ×S 3

Hu, Zejun; Yao, Zeke; Zhang, Yinshan

Mathematische Nachrichten, 02/2018, Volume: 291, Issue: 2-3

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In this paper, we study hypersurfaces of the homogeneous nearly Kähler manifold S 3 ×S 3 with typical properties. We first show that in the NK S 3 ×S 3 there exist neither totally umbilical hypersurfaces nor hypersurfaces of parallel second fundamental form. Then we investigate hypersurfaces of S 3 ×S 3 such that its shape operator A and induced almost contact structure satisfy the condition A = A, and as the main result, a complete classification of this remarkable family of hypersurfaces in S 3 ×S 3 is presented.

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