A Note on Some Generalized Curvature Tensor
Zafindratafa, Georges
Hotlos, Marian
Deszcz, Ryszard
Petrović-Torgašev, Miroslava
Glogowska, Malgorzata
Abstract: 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.
engleski
2023
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Keywords: warped product manifold; Einstein, quasi-Einstein and partially Einstein manifold; generalized Einstein metric condition; pseudosymmetry type curvature condition; Roter and generalized Roter space; hypersurface.