para-Kenmotsu Manifolds Research Articles

The Interesting Characterizations of Some Solitons in Lorentzian Para-Kenmotsu Manifolds

The Interesting Characterizations of Some Solitons in Lorentzian Para-Kenmotsu Manifolds

On LP-Kenmotsu Manifold with Regard to Generalized Symmetric Metric Connection of Type (α, β)

In the current article, we examine Lorentzian para-Kenmotsu (shortly, LP-Kenmotsu) manifolds with regard to the generalized symmetric metric connection ∇G of type (α,β). First, we obtain the expressions for curvature tensor, Ricci tensor and scalar curvature of an LP-Kenmotsu manifold with regard to the connection ∇G. Next, we analyze LP-Kenmotsu manifolds equipped with the connection ∇G that are locally symmetric, Ricci semi-symmetric, and φ-Ricci symmetric and also demonstrated that in all these situations the manifold is an Einstein one with regard to the connection ∇G. Moreover, we obtain some conclusions about projectively flat, projectively semi-symmetric and φ-projectively flat LP-Kenmotsu manifolds concerning the connection ∇G along with several consequences through corollaries. Ultimately, we provide a 5-dimensional LP-Kenmotsu manifold example to validate the derived expressions.

LP-Kenmotsu manifolds admitting Bach almost solitons

For an $LP$-Kenmotsu manifold of dimension $m$ (briefly, ${(LPK)_{m}}$) admitting Bach almost solitons $(g,\zeta,\lambda)$, we have explored the characteristics of norm of Ricci operator. Besides, we have studied the Bach tensor on Lorentzian para-Kenmotsu manifolds to have an $\eta$-Einstein manifold. Afterwards, we have proved that Bach almost solitons $(g,\zeta,\lambda)$ are always steady when, a Lorentzian para-Kenmotsu manifold of dimension-three has Bach almost solitons.

Quarter-symmetric metric connection on a p-Kenmotsu manifold

In the present paper we study para-Kenmotsu (p-Kenmotsu) manifold equipped with quarter-symmetric metric connection and discuss certain derivation conditions.

η-Ricci--Yamabe and *-η-Ricci--Yamabe solitons in Lorentzian para-Kenmotsu manifolds

Abstract The main purpose of this paper is to study η-Ricci–Yamabe solitons (η-RYS) and * {*} -η-Ricci–Yamabe solitons ( * {*} -η-RYS) in Lorentzian para-Kenmotsu n-manifolds (briefly, ( LPK ) n {(\mathrm{LPK})_{n}} ). We study the curvature condition R . S = 0 {R.S=0} and the cyclic parallel Ricci tensor in ( LPK ) n {(\mathrm{LPK})_{n}} admitting η-RYS. Furthermore, we study M-projectively flat and quasi-M-projectively flat Lorentzian para-Kenmotsu manifolds admitting * {*} -η-RYS. Finally, we give two examples of Lorentzian para-Kenmotsu manifolds admitting η-RYS and * {*} -η-RYS to verify some of our results.

On some important characterizations of Lorentz para-Kenmotsu manifolds on some special curvature tensors

In this paper, some properties of Lorentz para-Kenmotsu manifolds are studied using specified curvature tensors. The Lorentz para-Kenmotsu manifold is investigated in terms of the curvature tensors [Formula: see text] and [Formula: see text]. Initially, the tensor-based characterization of semisymmetric Lorentz para-Kenmotsu manifolds is studied. Subsequently, we consider the Lorentzian para-Kenmotsu manifold, which admits almost [Formula: see text]-Ricci solitons via these curvature tensors. According to the [Formula: see text] and [Formula: see text] curvature tensors, Ricci pseudosymmetry notions of Lorentzian para-Kenmotsu manifolds accepting [Formula: see text]-Ricci soliton have been developed. Following that, required conditions for the Lorentzian para-Kenmotsu manifold, admitting [Formula: see text]-Ricci soliton to be Ricci semisymmetric, are presented based on the curvature tensors chosen. Further, various characterizations are provided, and classifications are made under certain conditions. Finally, the characterizations of the invariant submanifolds of Lorentz para-Kenmotsu manifold on the [Formula: see text] and [Formula: see text] curvature tensors are investigated. We obtained the necessary and sufficient conditions for an invariant submanifold of a para-Kenmotsu to be [Formula: see text] and [Formula: see text] pseudoparallel.

RICCI SOLITONS ON Α-PARA KENMOTSU MANIFOLDS WITH SEMI SYMMETRIC METRIC CONNECTION

In this paper we introduce notion of Ricci solitons in -para Kenmotsu manifold with semi -symmetric metric connection. We have found the relations between curvature tensor, Ricci tensors and scalar curvature of -para Kenmotsu manifold with semi-symmetic metric connection.We have proved that 3-dimensional -para Kenmotsu manifold with semi -symmetric metric connection is an -Einstein manifold and the Ricci soliton defined on this manifold is named expanding and steady with respect to the value of constant.It is proved that Conharmonically flat -para Kenmotsu manifold with semi-symmetric metric connection is -Einstein manifold.

Conformal η-Ricci soliton in Lorentzian para Kenmotsu manifolds

The objective of the present paper is to study conformal η-Ricci soliton on Lorentzian Para-Kenmotsu manifolds with some curvature conditions. We study Concircular curvature tensor, Quasi conformal curvature tensor, Codazi type of Ricci tensor and cyclic parallel Ricci tensor in Lorentzian Para-Kenmotsu manifolds. At last we give examples of such manifolds.

Almost η-Ricci Solitons on the Pseudosymmetric Lorentzian Para-Kenmotsu Manifolds

In this paper, we consider Lorentzian para-Kenmotsu manifold admitting almost $\eta-$Ricci solitons by virtue of some curvature tensors. Ricci pseudosymmetry concepts of Lorentzian para-Kenmotsu manifolds admitting $\eta-$Ricci soliton have introduced according to the choice of some curvature tensors such as Riemann, concircular, projective, $\mathcal{M-}$projective, $W_{1}$ and $W_{2}.$ After then, according to the choice of the curvature tensors, necessary conditions are given for Lorentzian para-Kenmotsu manifold admitting $\eta-$Ricci soliton to be Ricci semisymmetric. Then some characterizations are given and classifications have made under the some conditions.

О связностях с кручением на неголономных пара-Кенмоцу многообразиях

The concept of a nonholonomic para-Kenmotsu manifold is intro­duced. A nonholonomic para-Kenmotsu manifold is a natural generaliza­tion of a para-Kenmotsu manifold; the distribution of a nonholonomic para-Kenmotsu manifold does not need to be involutive. Properly nonho­lonomic para-Kenmotsu manifolds are singled out, these are nonho­lono­mic para-Kenmotsu manifolds with non-involutive distribution. On an al­most (para-)contact metric manifold, we introduce a metric connec­tion with torsion, which is called a connection of Levi-Civita type in this pa­per. In the case of a nonholonomic para-Kenmotsu manifold, such a con­nection has a simpler structure than the Levi-Civita connection, and in so­me cases it turns out to be preferable from an applied point of view. A Le­vi-Civita type connection coincides with a Levi-Civita connec­tion if and only if a nonholonomic para-Kenmotsu manifold reduc­es to a para-Ken­motsu manifold. It is proved that a proper nonholonomic para-Ken­motsu manifold cannot carry the structure of an Einstein mani­fold with respect to a connection of the Levi-Civita type.

Anti-invariant and Clairaut anti-invariant pseudo-Riemannian submersions in para-Kenmotsu geometry

In this paper, we describe anti-invariant and Clairaut anti-invariant pseudo-Riemannian submersions (AIPR and CAIPR submersions, respectively, briefly) from para-Kenmotsu manifolds onto Riemannian manifolds. We introduce new Clairaut circumstances for anti-invariant submersions whose total space is para-Kenmotsu manifold. Also, we offer a obvious example of CAIPR submersion.

Conformal vector fields on N(k)-paracontact and para-Kenmotsu manifolds

Conformal vector fields on N(k)-paracontact and para-Kenmotsu manifolds

On generalized projective curvature tensor of para-Kenmotsu manifolds

On generalized projective curvature tensor of para-Kenmotsu manifolds

Certain properties of η-Ricci soliton on η-Einstein para-Kenmotsu manifolds

The objective of present research paper is to be investigate the geometric properties of ?-Ricci solitons on ?-Einstein para-Kenmotsu manifolds. In this manner, we consider ?-Ricci solitons on ?-Einstein para-Kenmotsu manifolds satistfying R.S = 0. Further, we obtain results for ?-Ricci solitons on ?-Einstein para-Kenmotsu manifolds with quasi-conformal flat property. Moreover, we get result for ?-Ricci solitins in ?-Einstein para-Kenmotsu manifolds admitting Codazzi type of Ricci tensor and cyclic parallel Ricci tensor, ?-quasi-conformally semi-symmetric, ?-Ricci symmetric and quasi-conformally Ricci semi-symmetric. At last, we construct an example of a such manifold which justify the existence of proper ?-Ricci solitons

A note on pseudoparallel submanifolds of Lorentzian para-Kenmotsu manifolds

In this article, pseudoparallel submanifolds for Lorentzian para-Kenmotsu manifolds are investigated. The Lorentzian para-Kenmotsu manifold is considered on the W1?curvature tensor. Submanifolds of these manifolds with properties such as W1?pseudoparallel, W1?2 pseudoparallel, W1?Ricci generalized pseudoparallel, and W1 ? 2 Ricci generalized pseudoparallel has been characterized.

Certain results of κ-almost gradient Ricci-Bourguignon soliton on pseudo-Riemannian manifolds

The prime object in this article is to study κ-almost Ricci-Bourguignon soliton and κ-almost gradient Ricci-Bourguignon soliton within the framework of paracontact metric manifolds. Here, we realize some conditions under which a paracontact metric manifold admitting a κ-Ricci–Bourguignon almost soliton is Einstein (trivial) and η-Einstein. We also show that if a three dimensional para-Kenmotsu manifold M3 admitting a κ-almost gradient Ricci-Bourguignon soliton with a constant scalar curvature, then the soliton becomes an almost gradient Ricci-Bourguignon soliton whose soliton function is −Ω. We also characterize and find some notable results κ-almost gradient Ricci-Bourguignon soliton on para-Sasakian manifolds and para-cosymplectic manifolds.

ON M-PROJECTIVE CURVATURE TENSOR OF PARA-KENMOTSU MANIFOLDS ADMITTING ZAMKOVOY CONNECTION

In this paper, relation between curvature tensors of Levi-Civita connection and Zamkovoy connection on para-Kenmotsu manifolds have been obtained.Quasi M-projectively flat, M-projectively flat and φ-M-projectively flat paraKenmotsu manifolds admitting Zamkovoy connection have been studied. Also, para-Kenmotsu manifolds admitting Zamkovoy connction satisfying M¯ (ξ, U).R¯ = 0 and M¯ (ξ, U).S¯ = 0 have been developed

Geometry of conformal η-Ricci solitons and conformal η-Ricci almost solitons on paracontact geometry

Abstract We prove that if an η \eta -Einstein para-Kenmotsu manifold admits a conformal η \eta -Ricci soliton then it is Einstein. Next, we proved that a para-Kenmotsu metric as a conformal η \eta -Ricci soliton is Einstein if its potential vector field V V is infinitesimal paracontact transformation or collinear with the Reeb vector field. Furthermore, we prove that if a para-Kenmotsu manifold admits a gradient conformal η \eta -Ricci almost soliton and the Reeb vector field leaves the scalar curvature invariant then it is Einstein. We also construct an example of para-Kenmotsu manifold that admits conformal η \eta -Ricci soliton and satisfy our results. We also have studied conformal η \eta -Ricci soliton in three-dimensional para-cosymplectic manifolds.

CERTAIN RESULTS ON $\eta$-RICCI SOLITIONS AND ALMOST $\eta$-RICCI SOLITONS

We prove that if an $\eta$-Einstein para-Kenmotsu manifold admits a $\eta$-Ricci soliton then it is Einstein. Next, we proved that a para-Kenmotsu metric as a $\eta$-Ricci soliton is Einstein if its potential vector field $V$ is infinitesimal paracontact transformation or collinear with the Reeb vector field. Further, we prove that if a para-Kenmotsu manifold admits a gradient almost $\eta$-Ricci soliton and the Reeb vector field leaves the scalar curvature invariant then it is Einstein. We also construct an example of para-Kenmotsu manifold that admits $\eta$-Ricci soliton and satisfy our results. We also have studied $\eta$-Ricci soliton in 3-dimensional normal almost paracontact metric manifolds and we show that if in a 3-dimensional normal almost paracontact metric manifold with $\alpha, \beta $ = constant, the metric is $\eta$-Ricci soliton, where potential vector field $V$ is collinear with the characteristic vector field $\xi$, then the manifold is $\eta$-Einstein manifold.

CHARACTERIZATIONS OF CONTACT PSEUDO-SLANT SUBMANIFOLDS OF A PARA-KENMOTSU MANIFOLD

In this paper, the geometry of contact pseudo-slant submanifolds of a para Kenmotsu manifold howe been studied. The necessary and sufficient conditions for a submanifolds to be a contact pseudoslant submanifolds of a para Kenmotsu manifold are given.