Ricci decomposition

About: Ricci decomposition is a research topic. Over the lifetime, 1972 publications have been published within this topic receiving 45295 citations.

Nonexistence of the Lanczos potential for the Riemann tensor in higher dimensions

Abstract: The existing refutal, in four-dimensional spacetimes, of the conjecture that the Lanczos tensor can be used as a potential for the Riemann tensor, is derived in a much simpler manner which is valid for dimension n ≥ 4 and any signature.

Tensor perturbations in a general class of Palatini theories

Abstract: We study a general class of gravitational theories formulated in the Palatini approach and derive the equations governing the evolution of tensor perturbations. In the absence of torsion, the connection can be solved as the Christoffel symbols of an auxiliary metric which is non-trivially related to the space-time metric. We then consider background solutions corresponding to a perfect fluid and show that the tensor perturbations equations (including anisotropic stresses) for the auxiliary metric around such a background take an Einstein-like form. This facilitates the study in a homogeneous and isotropic cosmological scenario where we explicitly establish the relation between the auxiliary metric and the space-time metric tensor perturbations. As a general result, we show that both tensor perturbations coincide in the absence of anisotropic stresses.

Classifications of kantowski–sachs, bianchi types i and iii spacetimes according to ricci collineations

Abstract: The Ricci collineation classifications of Kantowski–Sachs, Bianchi types I and III spacetimes are studied according to their degenerate and non-degenerate Ricci tensor. When the Ricci tensor is degenerate, the special cases are classified and it is shown that there are many cases of Ricci collineations (RCs) with infinite number of degrees of freedom, and the group of RCs is ten-dimensional in some spacial cases. Furthermore, it is found that when the Ricci tensor is non-degenerate, the group of RCs is finite-dimensional, and we have only either four which coincides with the isometries or six proper RCs in addition to the four isometries.

Differential geometry of quasi-Sasakian manifolds

Abstract: The full system of structure equations of a quasi-Sasakian structure is obtained. The structure of the main tensors on a quasi-Sasakian manifold (the Riemann-Christoffel tensor, the Ricci tensor, and other tensors) is studied on this basis. Interesting characterizations of quasi-Sasakian Einstein manifolds are obtained. Additional symmetry properties of the Riemann-Christoffel tensor are discovered and used for distinguishing a new class of quasi-Sasakian manifolds. An exhaustive description of the local structure of manifolds in this class is given. A complete classification (up to the -transformation of the metric) is obtained for manifolds in this class having additional properties of the isotropy kind.