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Hypersurfaces of the Homogeneous Nearly Kähler \(\mathbf {S}^3 \times \mathbf {S}^3\) with P-Invariant Holomorphic Distributions

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Abstract

In this paper, improving the results in [Ann Mat Pura Appl 199 (2020), 1147–1170] and [Manuscr Math, https://doi.org/10.1007/s00229-021-01308-4], we classify hypersurfaces of the homogeneous nearly Kähler manifold \(\mathbf {S}^3\times \mathbf {S}^3\) of which holomorphic distributions are preserved by the canonical almost product structure P of \(\mathbf {S}^3\times \mathbf {S}^3\). We also characterize these hypersurfaces as Hopf ones with constant Reeb functions and hypersurfaces with weakly \(\eta \)-parallel shape operators.

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Acknowledgements

The authors would like to thank the anonymous reviewers for their helpful and constructive comments that greatly contributed to improve the presentation of the paper.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, 450001, People’s Republic of China

    Zeke Yao, Xi Zhang & Zejun Hu

  2. Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, People’s Republic of China

    Zeke Yao

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  1. Zeke Yao
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  2. Xi Zhang
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  3. Zejun Hu
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Correspondence to Zejun Hu.

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This project was supported by NSF of China, Grant Number 12171437.

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Yao, Z., Zhang, X. & Hu, Z. Hypersurfaces of the Homogeneous Nearly Kähler \(\mathbf {S}^3 \times \mathbf {S}^3\) with P-Invariant Holomorphic Distributions. J Geom Anal 32, 209 (2022). https://doi.org/10.1007/s12220-022-00931-1

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