Affiliation:
1. Wroclaw University of Environmental and Life Sciences
2. State University of Novi Pazar, Department of Natural and Mathematical Sciences
3. Université Polytechnique Hauts-de-France
Abstract
The derivation-commutator
$R \cdot C - C \cdot R$ of a
semi-Riemannian manifold $(M,g)$, $\dim M \geq 4$, formed by its
Riemann-Christoffel curvature tensor
$R$ and the Weyl conformal curvature tensor $C$,
under some assumptions,
can be expressed
as a linear combination of $(0,6)$-Tachibana tensors $Q(A,T)$,
where $A$ is a symmetric $(0,2)$-tensor and $T$
a generalized curvature tensor. These conditions
form a family of generalized Einstein metric conditions.
In this survey paper we present recent results
on manifolds and submanifolds, and in particular hypersurfaces,
satisfying such conditions.
Publisher
International Electronic Journal of Geometry, Person (Kazim ILARSLAN)
Subject
Applied Mathematics,Geometry and Topology,Mathematical Physics