Gauss map and the topology of constant mean curvature hypersurfaces of \mathbbS⁷ and \mathbbCP³

2017/03/07 by Bittencourt, Fidelis, Fusieger, Pedro, Longa, Eduardo +1
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1703.02560

Abstract

We define a Gauss map γ:M→\mathbbS⁶ of an oriented hypersurface M of the unit sphere \mathbbS⁷ and prove that γ is harmonic if and only if M has CMC. Results on the geometry and topology of CMC hypersurfaces of \mathbbS⁷, under hypothesis on the image of γ, are then obtained. By a Hopf symmetrization process we define a Gauss map for hypersurfaces of \mathbbCP³ and obtain similar results for CMC hypersurfaces of this space.

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