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On some hypersurfaces of the homogeneous nearly Kähler S3×S3

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  • Zejun Hu
  • Zeke Yao
  • Yinshan Zhang

Abstract

In this paper, we study hypersurfaces of the homogeneous nearly Kähler manifold S3×S3 with typical properties. We first show that in the NK S3×S3 there exist neither totally umbilical hypersurfaces nor hypersurfaces of parallel second fundamental form. Then we investigate hypersurfaces of S3×S3 such that its shape operator A and induced almost contact structure ϕ satisfy the condition Aϕ=ϕA, and as the main result, a complete classification of this remarkable family of hypersurfaces in S3×S3 is presented.

Suggested Citation

  • Zejun Hu & Zeke Yao & Yinshan Zhang, 2018. "On some hypersurfaces of the homogeneous nearly Kähler S3×S3," Mathematische Nachrichten, Wiley Blackwell, vol. 291(2-3), pages 343-373, February.
    • Handle: RePEc:bla:mathna:v:291:y:2018:i:2-3:p:343-373
    DOI: 10.1002/mana.201600398
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