On hypersurfaces of $\mathbb{S}^2\times\mathbb{S}^2$

Francisco Urbano

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arXiv · 1606.07595

On hypersurfaces of $\mathbb{S}^2\times\mathbb{S}^2$

Francisco Urbano

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Abstract

We classify the homogeneous and isoparametric hypersurfaces of $\mathbb{S}^2\times\mathbb{S}^2$. In the classification, besides the hypersurfaces $\mathbb{S}^1(r)\times\mathbb{S}^2,\,r\in (0,1]$, it appears a family of hypersurfaces with three different constant principal curvatures and zero Gauss-Kronecker curvature. Also we classify the hypersurfaces of $\mathbb{S}^2\times\mathbb{S}^2$ with at most two constant principal curvatures and, under certain conditions, with three constant principal curvatures.

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BibTeX RIS

Francisco Urbano. 2016-06-24. On hypersurfaces of $\mathbb{S}^2\times\mathbb{S}^2$. https://arxiv.org/abs/1606.07595

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