Abstract
Our aim is to study invariant hypersurfaces immersed in the Euclidean space Rn+1, whose mean curvature is given as a linear function in the unit sphere Sn depending on its Gauss map. These hypersurfaces are closely related with the theory of manifolds with density, since their weighted mean curvature in the sense of Gromov is constant. In this paper we obtain explicit parametrizations of constant curvature hypersurfaces, and also give a classification of rotationally invariant hypersurfaces.
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