A Note on Some Generalized Curvature Tensor

Authors : Ryszard DESZCZ, Małgorzata GŁOGOWSKA, Marian HOTLOŚ, Miroslava PETROVİĆ-TORGAŠEV, Georges ZAFINDRATAFA

Pages : 379-397

Doi:10.36890/iejg.1273631

View : 6 | Download : 7

Publication Date : 2023-04-30

Article Type : Research Paper

Abstract :For any semi-Riemannian manifold insert ignore into journalissuearticles values(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 umbilica