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arXiv · 2409.12766

Weakly Einstein hypersurfaces in space forms

Jihun Kim·Yuri Nikolayevsky·JeongHyeong Park
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Abstract

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.

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Jihun Kim, Yuri Nikolayevsky, JeongHyeong Park. 2024-09-19. Weakly Einstein hypersurfaces in space forms. https://arxiv.org/abs/2409.12766

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