The objective of the present paper is to study 4-dimensional almost pseudo Ricci symmetric perfect fluid spacetimes $(APRS)_4$. We show that a Robertson-Walker spacetime $(APRS)_4$ and vice versa under certain condition imposed on its scale factor. Some popular toy models $F(R)$-gravity are also studied current setting various energy conditions investigated.

In this paper, we classify almost cosymplectic 3-manifolds with pseudo-parallel characteristic Jacobi operator. The only simply connected and complete non-cosymplectic 3-manifold pseudo parallel operator is the Minkowski motion group.

The idea to consider the concept of measure pseudo almost periodic oscillation corresponds better physical reality since periodicity is utopic. So, in this research paper, we inform a notion mu-pseudo-almost using theoretical measure. Then study existence and uniqueness pseudo-almost solutions some first-order differential equations Lebesgue spaces with variable exponents.

This article aims to study almost α-Kenmotsu pseudo-Riemannian structure. We first focus on the concept of structure and its basic properties. Then, we shall prove some fundamental formulas classification results such manifolds with CR-integrable Finally, illustrative examples manifold are given.