On real hypersurfaces of 𝕊²×𝕊²

Gao, Dong; Hu, Zejun; Ma, Hui; Yao, Zeke

doi:10.1090/proc/16116

On real hypersurfaces of $\mathbb {S}^2\times \mathbb {S}^2$
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by Dong Gao, Zejun Hu, Hui Ma and Zeke Yao PDF

Proc. Amer. Math. Soc. 150 (2022), 4447-4461 Request permission

Abstract:

In this paper, regarding the Riemannian product $\mathbb {S}^2\times \mathbb {S}^2$ of two unit $2$-spheres as a Kähler surface, we study its real hypersurfaces with typical geometric properties. First, we classify the real hypersurfaces of $\mathbb {S}^2\times \mathbb {S}^2$ with isometric Reeb flow and then, by using a Simons’ type inequality, a characterization of these compact real hypersurfaces is provided. Next, we classify Hopf hypersurfaces of $\mathbb {S}^2\times \mathbb {S}^2$ with constant product angle function. Finally, we classify Hopf hypersurfaces of $\mathbb {S}^2\times \mathbb {S}^2$ with parallel Ricci tensor.

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