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

Hu Zejun | Zendy; Yao Zeke | Zendy; Zhang Yinshan | Zendy

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

Author(s) -

Hu Zejun,

Yao Zeke,

Zhang Yinshan

Publication year - 2018

Publication title -

mathematische nachrichten

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.913

H-Index - 50

eISSN - 1522-2616

pISSN - 0025-584X

DOI - 10.1002/mana.201600398

Subject(s) - mathematics , homogeneous , pure mathematics , manifold (fluid mechanics) , kähler manifold , mathematical analysis , operator (biology) , combinatorics , chemistry , mechanical engineering , engineering , biochemistry , repressor , transcription factor , gene

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

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