2024/09/19 by Jihun Kim, Yuri Nikolayevsky, Kim, Jihun +3
Mathematics · Physics and Astronomy · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Advanced Differential Geometry Research
paper · pdf · doi:10.48550/arxiv.2409.12766
A Riemannian manifold (M,g) is called weakly Einstein if the tensor RiabcRj~~abc is a scalar multiple of the metric tensor gij. 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.