para-Sasakian Manifolds Research Articles

η-Ricci solitons and almost η-Ricci solitons on para-Sasakian manifolds

In this paper, we study para-Sasakian manifold [Formula: see text] whose metric [Formula: see text] is an [Formula: see text]-Ricci soliton [Formula: see text] and almost [Formula: see text]-Ricci soliton. We prove that, if [Formula: see text] is an [Formula: see text]-Ricci soliton, then either [Formula: see text] is Einstein and in such a case the soliton is expanding with [Formula: see text] or it is [Formula: see text]-homothetically fixed [Formula: see text]-Einstein manifold and in such a case the soliton is shrinking with [Formula: see text]. We show the same conclusion when the para-Sasakian manifold [Formula: see text] is of [Formula: see text] and [Formula: see text] is an almost [Formula: see text]-Ricci soliton with [Formula: see text] as infinitesimal contact transformation. Finally, we prove that, if the para-Sasakian manifold [Formula: see text] of [Formula: see text] admits a gradient almost [Formula: see text]-Ricci soliton with [Formula: see text], then [Formula: see text] is Einstein. Suitable examples are constructed to justify 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.

Para-Sasakian manifolds and $$*$$-Ricci solitons

In this paper we study a special type of metric called *-Ricci soliton on para-Sasakian manifold. We prove that if the para-Sasakian metric is a *-Ricci soliton on a manifold M, then M is either D-homothetic to an Einstein manifold, or the Ricci tensor of M with respect to the canonical paracontact connection vanishes.

Remarks on almost η-Ricci solitons in (ε)-para Sasakian manifolds

We consider almost η-Ricci solitons in (e)-para Sasakian manifolds satisfying certain curvature conditions. In the gradient case we give an estimation for the norm of the Ricci curvature tensor and express the scalar curvature of the manifold in terms of the two functions that define the soliton. We also prove that if the Ricci operator is of Codazzi type, then the gradient η-Ricci soliton is expanding if M is spacelike or shrinking if M is timelike.

Some Types of RICCI Solitons on Para-Sasakian Manifolds

Some Types of RICCI Solitons on Para-Sasakian Manifolds

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

A Note on Ricci Solitons on Para-Sasakian Manifolds

In the present paper, in an almost para-contact metric manifold, especially on para-Sasakian manifolds, Ricci solitons were examined. Also, we consider the generalized quasi-conformal curvature tensor on a para-Sasakian manifold admitting Ricci soliton.

Yamabe Solitons on Three-Dimensional N(k)-Paracontact Metric Manifolds

We prove that if a three-dimensional N(k)-paracontact metric manifold admits a Yamabe soliton $$(g,\xi )$$ , then the scalar curvature is constant and the manifold is a paraSasakian manifold. Moreover, we show that if a three-dimensional N(k)-paracontact metric manifold admits a Yamabe soliton (g, V), then either the manifold is a space of constant curvature, or the flow vector field V is Killing.

Lightlike hypersurfaces of an (ε)-para Sasakian manifold with a semi-symmetric non-metric connection

In the present paper, we study a lightlike hypersurface, when the ambient manifold is an (?)-para Sasakian manifold endowed with a semi-symmetric non-metric connection. We obtain a condition for such a lightlike hypersurface to be totally geodesic. We define invariant and screen semi-invariant lightlike hypersurfaces of (?)-para Sasakian manifolds with a semi-symmetric non-metric connection. Also, we obtain integrability conditions for the distributions D ? ??? and D' ? ??? of a screen semi-invariant lightlike hypersurface of an (?)-para Sasakian manifolds with a semi-symmetric non-metric connection.

On anti-invariant semi-Riemannian submersions from Lorentzian para-Sasakian manifolds

In this paper, we study a semi-Riemannian submersion from Lorentzian almost (para) contact manifolds and find necessary and sufficient conditions for the characteristic vector field to be vertical or horizontal. We also obtain decomposition theorems for anti-invariant semi-Riemannian submersions from Lorentzian para-Sasakian manifolds onto Lorentzian manifolds.

Some Properties of Para-Sasakian Manifolds

In this paper author present an investigation of some differential geometric properties of Para-Sasakian manifolds. Condition for a vector field to be Killing vector field in Para-Sasakian manifold is obtained. Mathematics Subject Classification (2010). 53B20, 53C15.

Certain results on K-paracontact and paraSasakian manifolds

The purpose of this paper is to study 3-dimensional paraSasakian manifold and conformally flat K-paracontact manifold. Moreover, we show that in a K-paracontact manifold the conditions Einstein, conformally flat, semi-symmetric and Ricci semi-symmetric are all equivalent. Finally, compact regular 3-dimensional paraSasakian and conformally flat K-paracontact manifolds are studied.

On para-sasakian manifolds satisfying certain curvature conditions

In this paper, we investigate Ricci pseudo-symmetric and Ricci generalized pseudo-symmetric P-Sasakian manifolds. Next we study P-Sasakian manifolds satisfying the curvature condition S ? R = 0. Finally, we give an example of a 5-dimensional P-Sasakian manifold to verify some results.

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

$${\eta}$$ η -Ricci solitons on para-Sasakian manifolds

The object of this paper is to study a special type of metrics called \({\eta}\)-Ricci solitons on para-Sasakian manifolds. We give the existence of para-Sasakian \({\eta}\)-Ricci solitons in our settings. In addition, the non-existence of certain geometric characteristics of para-Sasakian \({\eta}\)-Ricci solitons are studied. Finally, we discuss 3-dimensional and conformally flat para-Sasakian \({\eta}\)-Ricci solitons.

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.

On para-Sasakian manifolds with a canonical paracontact connection

The object of the present paper is to study a para-Sasakian manifold with a canonical paracontact connection. We prove that ϕ−conformally flat, ϕ−concircularly flat and ϕ−projectively flat para-Sasakian manifolds with respect to c anonical paracontact connection are all η−Einstein manifolds. Also, it is shown that a quasi-concircularly flat para-Sasakian manifold is of constant scalar curvature.

Para-Sasakian manifolds satisfying certain curvature conditions

In this paper, we investigate P-Sasakian manifolds satisfying the conditions R(X, ξ) · C = 0 and $$C \cdot \widetilde Z = 0$$ , where C and $$\widetilde Z$$ are the Weyl conformal curvature tensor and the concircular curvature tensor respectively. Next, we study 3-dimensional P-Sasakianmanifolds. Finally, we give an example of a 3-dimensional P-Sasakian manifold.