Some geometric and physical properties of pseudo Ψ-symmetric manifolds

Abstract

In this article, we present a new tensor that generalizes the conharmonic curvature tensor, termed the Ψ-conharmonic curvature tensor. In the first part, we derive some fundamental geometrical properties of a pseudo Ψ-conharmonically symmetric manifold (briey, (PCS)_n) and give some fascinating outcomes. Among others, we establish that an Einstein (PCS)n (n > 2) manifold is of zero scalar curvature. Besides, we investigate Ψ-conharmonically at perfect fluid and (PCS)₄ spacetimes, respectively. As a result, we acquire some significant theorems. Finally, we construct several non-trivial examples to establish the existence of (PCS)₄.