Some geometric and physical properties of pseudo ψ-conharmonically symmetric manifolds

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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 (briefly, ) and give some fascinating outcomes. Among others, we establish that an Einstein manifold is of zero scalar curvature. Besides, we investigate ψ-conharmonically flat perfect fluid and spacetimes, respectively. As a result, we acquire some significant theorems. Finally, we construct several non-trivial examples to establish the existence of .