Lorentzian para-Sasakian Manifolds Research Articles

ON QUASI BI-SLANT RIEMANNIAN MAPS FROM LORENTZIAN PARA SASAKIAN MANIFOLDS

We first introduce quasi bi-slant Riemannian maps and study such Riemannian maps from Lorentzian para Sasakian manifolds into Riemannian manifolds. We give necessary and sufficient conditions for the integrability of the distributions which are involved in the definition of the quasi bi-slant Riemannian map and investigate their leaves. We also obtain totally geodesic conditions for such maps. Moreover, we provide some examples for this notion.

Lorentzian Para-Sasakian Manifolds and *-Ricci Solitons

We study the properties of Lorentzian para-Sasakian manifolds endowed with ∗-Ricci solitons and gradient ∗-Ricci solitons. Finally, the existence of ∗-Ricci soliton on a 4-dimensional Lorentzian para-Sasakian manifold is proved by constructing a non-trivial example

Certain Results on the Lifts from an LP-Sasakian Manifold to Its Tangent Bundle Associated with a Quarter-Symmetric Metric Connection

The purpose of this study is to examine the complete lifts from the symmetric and concircular symmetric n-dimensional Lorentzian para-Sasakian manifolds (briefly, (LPS)n) to its tangent bundle TM associated with a Riemannian connection DC and a quarter-symmetric metric connection (QSMC) D¯C.

Properties of Anti-Invariant Submersions and Some Applications to Number Theory

In this article, we investigate anti-invariant Riemannian and Lagrangian submersions onto Riemannian manifolds from the Lorentzian para-Sasakian manifold. We demonstrate that, for these submersions, horizontal distributions are not integrable and their fibers are not totally geodesic. As a result, they are not totally geodesic maps. The harmonicity of such submersions is also examined. We specifically prove that they are not harmonic when the Reeb vector field is horizontal. Finally, we provide an illustration of our findings and mention some number-theoretic applications for the same submersions.

On Quasi Hemi-Slant Submersions

The paper deals with the notion of quasi hemi-slant submersions from Lorentzian para Sasakian manifolds onto Riemannian manifolds. These submersions are generalization of hemi-slant submersions and semi-slant submersions. In this paper, we also study the geometry of leaves of distributions which are involved in the definition of the submersion. Further, we obtain the conditions for such distributions to be integrable and totally geodesic. Moreover, we also give the characterization theorems for proper quasi hemi-slant submersions and provide some examples of it.

On $(epsilon)$ - Lorentzian para-Sasakian Manifolds

The object of this paper is to study $(epsilon)$-Lorentzian para-Sasakian manifolds. Some typical identities for the curvature tensor and the Ricci tensor of $(epsilon)$-Lorentzian para-Sasakian manifold are investigated. Further, we study globally $phi$-Ricci symmetric and weakly $phi$-Ricci symmetric $(epsilon)$-Lorentzian para-Sasakian manifolds and obtain interesting results.

Geodesic Lightlike Submanifolds of Lorentzian Para-Sasakian Manifolds

In this paper we study invariant lightlike submanifolds of Lorentzian para-sasakian manifolds. We investigate geodesic CR-lightlike submanifolds of Lorentzian para-sasakian manifolds. We study screen CR-lightlike submanifolds of Lorentzian para-sasakian manifolds. Some necessary and sufficient conditions for mixed geodesic, totally geodesic, -geodesic and -geodesic contact CR-lightlike submanifolds and SCR-lightlike submanifolds are obtained.

Sesqui-Harmonic Curves in LP-Sasakian Manifolds

In this article, we characterize interpolating sesqui-harmonic spacelike curves in a four dimensional conformally and quasi-conformally flat and conformally symmetric Lorentzian Para-Sasakian manifold. We give some theorems for these curves.

Projective Curvature Tensor with Respect to Zamkovoy Connection in Lorentzian Para-Sasakian Manifolds

The purpose of the present paper is to study some properties of the Projective curvature tensor with respect to Zamkovoy connection in Lorentzian Para Sasakian manifold(or,LP-Sasakian manifold)'And we have studied some results in Lorentzian Para-Sasakian manifold with the help of Zamkovoy connection and Projective curvature tensor.Also we discussed the LP-Sasakian manifold satisfying P*(ξ,U)∘W₀*=0,P*(ξ,U)∘W₂*=0 , where W₀*,W₂* and P* are W₀,W₂ and Projective curvature tensors with respect to Zamkovoy connection.

Eta-Ricci soliton on W3-Semi symmetric LP Sasakian Manifolfds

In this paper, we study ƞ-Ricci solitons on Lorentzian para-Sasakian manifold satisfying the semi symmetric conditions R(ξ,X)•W3 (Y,Z) U=0 and W3 (ξ,X)•R(Y,Z)U=0. At the end of this paper, we show that the LP-Sasakian manifold accepting a ƞ-Ricci solitons structure is Einstain.

F−BIHARMONIC CURVES WITH TIMELIKE NORMAL VECTOR ON LORENTZIAN SPHERE

In this paper, we study $f-$biharmonic curves as the critical points of the $f-$bienergy functional $E_{2}(\psi )=\int_{M}f\mid \tau (\psi )^{2}\mid \vartheta _{g}$, on a Lorentzian para-Sasakian manifold $M$. We give necessary and sufficient conditions for a curve such that has a timelike principal normal vector on lying a $4$-dimensional conformally flat, quasi-conformally flat and conformally symmetric Lorentzian para-Sasakian manifold to be an $f-$biharmonic curve. Moreover, we introduce proper $f-$biharmonic curves on the Lorentzian sphere $S_{1}^{4}.$

On Ricci solitons in LP-Sasakian manifolds

In this paper we study Ricci solitons in Lorentzian para-Sasakian manifolds. It is proved that the Ricci soliton in a (2n+1)-dimensinal LP-Sasakian manifold is shrinking. It is also shown that Ricci solitons in an LP-Sasakian manifold satisfying the derivation conditions R(ξ,X).W2 =0,W2 (ξ,X).W4 =0 and W4 (ξ,X).W2=0 are shrinking but are steady for the condition W2 (ξ,X).S=0. Finally, we give an example of 3-dimensional LP-Sasakian manifold and prove that the Ricci soliton is expanding and shrinking in this manifold.
 BIBECHANA 17 (2020) 110-116

Lorentzian para-Sasakian Manifolds Admitting a New Type of Quarter-symmetric Non-metric ξ-connection

We define a new type of quarter-symmetric non-metric $\xi$-connection on an $LP$-Sasakian manifold and prove its existence. We provide its application in the general theory of relativity. To validate the existence of the quarter-symmetric non-metric $\xi$-connection on an $LP$-Sasakian manifold, we give a non-trivial example in dimension $4$ and verify our results.

Eta-Ricci solitons on LP-Sasakian manifolds

We consider η-Ricci solitons on Lorentzian para-Sasakian manifolds with Codazzi type of the Ricci tensor. Then we study η-Ricci solitons on ϕ-conformally semi-symmetric, ϕ-Ricci symmetric, and conformally Ricci semi-symmetric Lorentzian para-Sasakian manifolds. Finally, we construct an example of a three dimensional Lorentzian para-Sasakian manifold which admits η-Ricci solitons with non-constant scalar curvature.

Characterization of the Lorentzian para-Sasakian manifolds admitting a quarter-symmetric non-metric connection

We set the goal to study the properties of LP-Sasakian manifolds equipped with a quarter-symmetric non-metric connection. It is proved that the LP-Sasakian manifold endowed with a quarter-symmetric non-metric connection is partially Ricci semisymmetric with respect to the quarter-symmetric non-metric connection if and only if it is an η-Einstein manifold. We also study the properties of semisymmetric, Ricci recurrent LP-Sasakian manifolds and η-parallel Ricci tensor with respect to the quarter-symmetric non-metric connection. In the end, the non-trivial example of a 4-dimensional LP-Sasakian manifold with a quarter-symmetric non-metric connection is given.

On some classes of concircular curvature tensor on Lorentzian para-Sasakian manifolds

The present paper deals with the study of different classes of concircular curvature tensor on Lorentzian para-Sasakian manifold admitting a quarter-symmetric metric connection.

SOME TYPES OF η-RICCI SOLITONS ON LORENTZIAN PARA-SASAKIAN MANIFOLDS

In this paper we study some types of η-Ricci solitons on Lorentzianpara-Sasakian manifolds and we give an example of η-Ricci solitons on 3-dimensional Lorentzian para-Sasakian manifold. We obtain the conditions of η-Ricci soliton on ϕ-conformally flat, ϕ-conharmonically flat and ϕ-projectivelyflat Lorentzian para-Sasakian manifolds, the existence of η-Ricci solitons implies that (M,g) is η-Einstein manifold. In these cases there is no Ricci solitonon M with the potential vector field

On a Lorentzian para-Sasakian manifold with respect to the quarter-symmetric metric connection

On a Lorentzian para-Sasakian manifold with respect to the quarter-symmetric metric connection

On some classes of invariant submanifolds of lorentzian para-sasakian manifolds

The object of the present paper is to study invariant submanifolds of Lorenzian Para-Sasakian manifolds. We consider the recurrent and bi-recurrent invariant submanifolds of Lorentzian para-Sasakian manifolds and pseudo-parallel and generalized Ricci pseudo-parallel invariant submanifolds of Lorentzian para-Sasakian manifolds. Also we search for the conditions $\mathcal{Z}(X,Y)\cdot\alpha=fQ(g,\alpha)$ and $\mathcal{Z}(X,Y)\cdot\alpha=fQ(S,\alpha)$ on invariant submanifolds of Lorentzian para-Sasakian manifolds, where $\mathcal{Z}$ is the concircular curvature tensor. Finally, we construct an example of an invariant submanifold of Lorentzian para Sasakian manifold.

Lorentzian para-Sasakian manifold with quarter-symmetric non-metric connection

The object of the present paper is to study quarter symmetric nonmetric connection on a LP-Sasakian manifold. In this paper, we consider some properties of the curvature tensor, projective curvature tensor, concircular curvature tensor, conformai curvature tensor with respect to quarter symmetric non-metric connection in a LP-Sasakian manifolds. Finally we consider submanifolds with respect to quarter symmetric non-metric connection.