On Concircular Curvature Tensor in Space-Times

Abstract

The aim of this work is to examine some properties of the concircular curvature tensor on $4-$dimensional manifolds admitting a Lorentz metric (so called space-times). In the first two sections, the study is introduced and the interrelated concepts together with some notations are presented. In the third section of the study, some results are obtained connected to eigenbivector structure of the concircular curvature tensor on these manifolds by taking into account the classification scheme of 2--forms (also known as bivectors) in this metric signature. Then, the known holonomy algebras on space-times are considered and some theorems are given regarding the concircular and Riemann curvature tensors. This analysis is also associated with the types of the Riemann curvature tensor on these manifolds. In the last section, the results of the study is summarized and the discussion part is presented.