A Note on Some Generalized Curvature Tensor

For any semi-Riemannian manifold (M, g) we define some generalized curvature tensor E as a linear combination of Kulkarni-Nomizu products formed by the metric tensor, the Ricci tensor and its square of given manifold. That tensor is closely related to quasi-Einstein spaces, Roter spaces and some Roter type spaces.

Keywords:

warped product manifold, Einstein manifold, quasi-Einstein manifold, partially Einstein manifold, generalized Einstein metric condition, pseudosymmetry type curvature condition Roter space, generalized Roter space, hypersurface, principal curvature, quasi-umbilical hypersurface,

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