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In this paper, we study left-invariant cross curvature solitons on Lorentzian three-dimensional Lie groups and classify these solitons. [ABSTRACT FROM AUTHOR]

The aim of this paper is to characterize a Riemannian 3-manifold M 3 equipped with a semi-symmetric metric ξ -connection ∇ ˜ with ρ -Einstein and gradient ρ -Einstein solitons. The existence of a gradient ρ -Einstein soliton in an M 3 admitting ∇ ˜ is ensured by constructing a non-trivial example, and hence some of our results are verified. By using standard tensorial technique, we prove that the scalar curvature of (M 3 , ∇ ˜) satisfies the Poisson equation Δ R = 4 (2 − σ − 6 ρ) ρ . [ABSTRACT FROM AUTHOR]

The present paper deals with the investigations of a Kenmotsu manifold satisfying certain curvature conditions endowed with - η -Ricci solitons. First we find some necessary conditions for such a manifold to be φ -Einstein. Then, we study the notion of - η -Ricci soliton on this manifold and prove some significant results related to this notion. Finally, we construct a nontrivial example of three-dimensional Kenmotsu manifolds to verify some of our results. [ABSTRACT FROM AUTHOR]

In this note, the generalized Lorentzian Sasakian-space-form M 1 2 n + 1 (f 1 , f 2 , f 3) satisfying certain constraints on the M -projective curvature tensor W * is considered. Here, we characterize the structure M 1 2 n + 1 (f 1 , f 2 , f 3) when it is, respectively, M -projectively flat, M -projectively semisymmetric, M -projectively pseudosymmetric, and φ − M -projectively semisymmetric. Moreover, M 1 2 n + 1 (f 1 , f 2 , f 3) satisfies the conditions W * (ζ , V 1) · S = 0 , W * (ζ , V 1) · R = 0 and W * (ζ , V 1) · W * = 0 are also examined. Finally, illustrative examples are given for obtained results. [ABSTRACT FROM AUTHOR]

In the present note, we study ϵ -LP-Sasakian 3-manifolds M 3 ϵ whose metrics are conformal η -Ricci-Yamabe solitons (in short, CERYS), and it is proven that if an M 3 ϵ with a constant scalar curvature admits a CERYS, then £ U ζ is orthogonal to ζ if and only if Λ − ϵ σ = − 2 ϵ l + m r / 2 + 1 / 2 p + 2 / 3 . Further, we study gradient CERYS in M 3 ϵ and proved that an M 3 ϵ admitting gradient CERYS is a generalized conformal η -Einstein manifold; moreover, the gradient of the potential function is pointwise collinear with the Reeb vector field ζ. Finally, the existence of CERYS in an M 3 ϵ has been drawn by a concrete example. [ABSTRACT FROM AUTHOR]

The object of the present paper is to study 3-dimensional f -Kenmotsu manifolds with respect to the semi-symmetric metric connection satisfying certain curvature conditions. Finally, we give an example of 3-dimensional f -Kenmotsu manifolds. [ABSTRACT FROM AUTHOR]

In the present paper, we have studied η-Ricci solitons in Lorentzian α-Sasakian manifolds satisfying certain curvature conditions. The existence of η-Ricci soliton in a Lorentzian α-Sasakian manifold has been proved by a concrete example. [ABSTRACT FROM AUTHOR]

The curvature properties of three-dimensional f-Kenmotsu manifolds have been studied. [ABSTRACT FROM AUTHOR]

The object of the present paper is to study generalized Sasakian-space-forms satisfying the curvature condition P(ξ, Y) - W = 0. Moreover, ø-M-projectively semisymmetric and ø-pseudo-projectively semisymmetric generalized Sasakian-space-forms are also studied. [ABSTRACT FROM AUTHOR]

The objective of the present paper is to study some new results on quasi-conformal curvature tensor in a Kenmotsu manifold with respect to a semi-symmetric non-metric connection. [ABSTRACT FROM AUTHOR]

The objective of the present paper is to study some new results on concircular curvature tensor in a Kenmotsu manifold with respect to the semi-symmetric non-metric connection. [ABSTRACT FROM AUTHOR]