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On Hopf hypersurfaces of the homogeneous nearly Kähler \({\mathbf {S}}^3\times {\mathbf {S}}^3\), II

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In this sequel to our article on Hopf hypersurfaces of the homogeneous NK (nearly Kähler) manifold \({\mathbf {S}}^3\times {\mathbf {S}}^3\) (Hu and Yao in Ann Mat Pura Appl, 199:1147–1170, 2020), we continue working on the problem of determining the Hopf hypersurfaces of this ambient space for which the holomorphic distributions are preserved by the almost product structure of \({\mathbf {S}}^3\times {\mathbf {S}}^3\). As complements to existing results, we first show that no such Hopf hypersurfaces admit exactly four distinct principal curvatures. Then, as the second main result and an important step towards the solution of the preceding problem, we establish a complete classification of such Hopf hypersurfaces with five distinct constant principal curvatures.

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Acknowledgements

The authors are much indebted to the referee for his/her valuable comments which impel us to have modified the original version so that Remarks 1.4 and 4.1 are added.

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

    Zeke Yao & Zejun Hu

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  1. Zeke Yao
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  2. Zejun Hu
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Correspondence to Zejun Hu.

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This project was supported by NSF of China, Grant Number 11771404

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Yao, Z., Hu, Z. On Hopf hypersurfaces of the homogeneous nearly Kähler \({\mathbf {S}}^3\times {\mathbf {S}}^3\), II. manuscripta math. 168, 371–402 (2022). https://doi.org/10.1007/s00229-021-01308-4

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  • DOI: https://doi.org/10.1007/s00229-021-01308-4

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