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We define a Gauss map $\gamma:M\rightarrow\mathbb{S}^{6}$ of an orientedhypersurface $M$ of the unit sphere $\mathbb{S}^{7}$ and prove that $\gamma$ isharmonic if and only if $M$ has CMC. Results on the geometry and topology ofCMC hypersurfaces of $\mathbb{S}^{7}$, under hypothesis on the image of$\gamma$, are then obtained. By a Hopf symmetrization process we define a Gaussmap for hypersurfaces of $\mathbb{CP}^{3}$ and obtain similar results for CMChypersurfaces of this space.

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