Weakly Einstein hypersurfaces in space forms
Abstract
A Riemannian manifold ( M , g ) is called weakly Einstein if the tensor R i a b c R j a b c is a scalar multiple of the metric tensor g i j . 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.
Fields of Study & Subjects
Advanced Differential Geometry Research
Geometric Analysis and Curvature Flows
Geometry and complex manifolds
Publication details
- Journal / source
- Differential Geometry and its Applications
- Volume
- 103
- Pages
- 102350–102350
- Publication date
- 12 February 2026
- Language
- EN