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In this paper, we investigate Ricci–Yamabe solitons (RYSs) and gradient Ricci–Yamabe solitons (gradient RYSs) in generalized Robertson–Walker (GRW) spacetimes. At first, we prove that if a GRW spacetime admits a RYS, then it becomes a perfect fluid spacetime (PFS) and the divergence of the Weyl tensor vanishes. Also, a GRW spacetime admitting a RYS is of Petrov type I , D or O and in case of four dimension, the spacetime turns into a Robertson–Walker spacetime. Next, we show that if a GRW spacetime of constant scalar curvature admits a gradient RYS, then it becomes a PFS and the divergence of the Weyl tensor vanishes. [ABSTRACT FROM AUTHOR]

In this article, we initiate the study of conformal vector fields in paracontact geometry. First, we establish that if the Reeb vector field ζ is a conformal vector field on N(k)-paracontact metric manifold, then the manifold becomes a para-Sasakian manifold. Next, we show that if the conformal vector field V is pointwise collinear with the Reeb vector field ζ, then the manifold recovers a para-Sasakian manifold as well as V is a constant multiple of ζ. Furthermore, we prove that if a 3-dimensional N(k)-paracontact metric manifold admits a Killing vector field V, then either it is a space of constant sectional curvature k or, V is an infinitesimal strict paracontact transformation. Besides these, we also investigate conformal vector fields on para-Kenmotsu manifolds. [ABSTRACT FROM AUTHOR]

In this paper, we characterize Ricci–Yamabe solitons and gradient Ricci–Yamabe solitons on 3-dimensional generalized Sasakian space forms with quasi Sasakian metric. Furthermore, we study η -Ricci–Yamabe solitons and gradient η -Ricci–Yamabe solitons on 3-dimensional generalized Sasakian space forms with quasi Sasakian metric. Finally, we construct an example to verify a result of our paper. [ABSTRACT FROM AUTHOR]

The aim of this paper is to characterize a Kenmotsu 3-manifold whose metric is either a Ricci-Yamabe soliton or gradient Ricci-Yamabe soliton. Finally, we verify the obtained results by an example. [ABSTRACT FROM AUTHOR]

We have studied curvature symmetries in (∈)-Kenmotsu manifolds. Next, we have proved the non-existence of a non-zero parallel 2-form in an (∈)-Kenmotsu manifold. Moreover, we have characterised Φ-Ricci symmetric (∈)-Kenmotsu manifolds and finally, we have proved that under certain restriction on the scalar curvature divR=0 and divC=0 are equivalent, where 'div' denotes divergence. [ABSTRACT FROM AUTHOR]

The object of the present paper is to characterize LP-Sasakian manifolds satisfying Ricci pseudosymmetry and Ricci generalized pseudosymmetry. Beside this we prove that if R(X; ξ):P = P(X; ξ):R holds, where R and P denote the curvature tensor and projective curvature tensor respectively, then the manifold becomes an Einstein manifold. Then we prove that divR = 0 and divC = 0 are equivalent if the scalar curvature is invariant under the characteristic vector field ξ, where 'div' denotes divergence. Finally, we characterize 3-dimensional LP-Sasakian manifolds admitting Yamabe solitons and prove that the scalar curvature is constant and the potential vector field V is Killing. [ABSTRACT FROM AUTHOR]