A Riemannian manifold $(M,g)$ is called \emph{ weakly Einstein} if the tensor $R_{ iabc}R_{ j}^{ ~~abc}$ is a scalar multiple of the metric tensor $g_{ ij}$. We give a complete classification of weakly Einstein hypersurfaces in the spaces of nonzero constant curvature (the classification in a Euclidean space has been previously known). The main result states that such a hypersurface can only be the product of two spaces of constant curvature or a rotation hypersurface.
Categories: math.DG