On hypersurfaces of \mathbbS²×\mathbbS²

2016/06/24 by Urbano, Francisco
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1606.07595

Abstract

We classify the homogeneous and isoparametric hypersurfaces of \mathbbS²×\mathbbS². In the classification, besides the hypersurfaces \mathbbS¹(r)×\mathbbS², r∈ (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 \mathbbS²×\mathbbS² with at most two constant principal curvatures and, under certain conditions, with three constant principal curvatures.

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