Gauss map and the topology of constant mean curvature hypersurfaces of ${\mathbb{S}}^7$ and ${\mathbb{CP}}^3$

Fidelis Bittencourt, Pedro Fusieger, Eduardo Longa +1

We define a Gauss map $\gamma :M\to {\mathbb{S}}^6$ of an oriented hypersurface $M$ of the unit sphere ${\mathbb{S}}^7$ and prove that $\gamma$ is harmonic if and only if $M$ has CMC.…