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The current work first explores projective collineations on pseudo-Riemannian manifolds. Projective collineations, curvature collineations, and Ricci curvature collineations are examined in relation to one another. On warped product manifolds, the projective collineations of the form ζ = ζ 1 + ζ 2 are investigated. We scrutinize various inheritance aspects in projective collineations from warped product manifolds to its factor manifolds. This provides, for example, a partially negative solution to Besse's problem regarding the existence of Einstein warped product manifolds. Finally, Pseudo-Ricci symmetric space-times admitting projective collineations are investigated. [ABSTRACT FROM AUTHOR]

In this work, we have characterized the frame bundle F M admitting metallic structures on almost quadratic ϕ -manifolds ϕ 2 = p ϕ + q I − q η ⊗ ζ , where p is an arbitrary constant and q is a nonzero constant. The complete lifts of an almost quadratic ϕ -structure to the metallic structure on F M are constructed. We also prove the existence of a metallic structure on F M with the aid of the J ˜ tensor field, which we define. Results for the 2-Form and its derivative are then obtained. Additionally, we derive the expressions of the Nijenhuis tensor of a tensor field J ˜ on F M . Finally, we construct an example of it to finish. [ABSTRACT FROM AUTHOR]

A conformally flat GRW space-time is a perfect fluid RW space-time. In this note, we investigated the influence of many differential curvature conditions, such as the existence of recurrent and semi-symmetric curvature tensors. In each case, the form of the Ricci curvature tensor, the energy–momentum tensor, the energy density, the pressure of the fluid, and the equation of state are determined and interpreted. For example, it is demonstrated that a Ricci semi-symmetric RW space-time reduces to Einstein space-time or a Ricci recurrent RW space-time, and the perfect fluid space-time is referred to as Yang pure space-time or dark matter era. [ABSTRACT FROM AUTHOR]

The objective of this paper is to explore the complete lifts of a quarter-symmetric metric connection from a Sasakian manifold to its tangent bundle. A relationship between the Riemannian connection and the quarter-symmetric metric connection from a Sasakian manifold to its tangent bundle was established. Some theorems on the curvature tensor and the projective curvature tensor of a Sasakian manifold with respect to the quarter-symmetric metric connection to its tangent bundle were proved. Finally, locally ϕ -symmetric Sasakian manifolds with respect to the quarter-symmetric metric connection to its tangent bundle were studied. [ABSTRACT FROM AUTHOR]

In this article, we classify h-almost Ricci–Yamabe solitons in paracontact geometry. In particular, we characterize para-Kenmotsu manifolds satisfying h-almost Ricci–Yamabe solitons and 3-dimensional para-Kenmotsu manifolds obeying h-almost gradient Ricci–Yamabe solitons. Then, we classify para-Sasakian manifolds and para-cosymplectic manifolds admitting h-almost Ricci–Yamabe solitons and h-almost gradient Ricci–Yamabe solitons, respectively. Finally, we construct an example to illustrate our result. [ABSTRACT FROM AUTHOR]

This paper investigates singly warped product manifolds admitting semi-conformal curvature tensors. The form of the Riemann tensor and Ricci tensor of the base and fiber manifolds of a semi-conformally flat singly warped product manifold are provided. It is demonstrated that the fiber manifold of a semi-conformally flat warped product manifold has a constant curvature. Sufficient requirements on the warping function to ensure that the base manifold is a quasi-Einstein or an Einstein manifold are provided. [ABSTRACT FROM AUTHOR]

The lifts of Sasakian statistical manifolds associated with a semi-symmetric metric connection in the tangent bundle are characterized in the current research. The relationship between the complete lifts of a statistical manifold with semi-symmetric metric connections and Sasakian statistical manifolds with a semi-symmetric metric connection in the tangent bundle is investigated. We also discuss the classification of Sasakian statistical manifolds with respect to semi-symmetric metric connections in the tangent bundle. Finally, we derive an example of the lifts of Sasakian statistical manifolds to the tangent bundle. [ABSTRACT FROM AUTHOR]

The subject of the present paper is the investigation of a new type of solitons, called η -∗-Ricci solitons in (k , μ) -almost co-Kähler manifold (briefly, a c k m ), which generalizes the notion of the η -Ricci soliton introduced by Cho and Kimura. First, the expression of the ∗-Ricci tensor on a c k m is obtained. Additionally, we classify the η -∗-Ricci solitons in (k , μ) - a c k m s. Next, we investigate (k , μ) - a c k m s admitting gradient η -∗-Ricci solitons. Finally, we construct two examples to illustrate our results. [ABSTRACT FROM AUTHOR]