Schouten-van Kampen Connection Research Articles

Characterization of Almost \(\eta\) -Ricci Solitons With Respect to Schouten-van Kampen Connection on Sasakian Manifolds

In this paper, we investigate Sasakian manifolds that admit almost \(\eta\) -Ricci solitons with respect to the Schouten-van Kampen connection using certain curvature tensors. Concepts of Ricci pseudosymmetry for Sasakian manifolds admitting \(\eta\)-Ricci solitons are introduced based on the selection of specific curvature tensors such as Riemann, concircular, projective, pseudo-projective, M-projective, and W2 tensors. Subsequently, necessary conditions are established for a Sasakian manifold admitting \(\eta\)-Ricci soliton with respect to the Schouten-van Kampen connection to be Ricci semisymmetric, based on the choice of curvature tensors. Characterizations are then derived, and classifications are made under certain conditions.

Optimal Inequalities on (α,β)-Type Almost Contact Manifold with the Schouten–Van Kampen Connection

In the current research, we develop optimal inequalities for submanifolds in trans-Sasakian manifolds or (α,β)-type almost contact manifolds endowed with the Schouten–Van Kampen connection (SVK-connection), including generalized normalized δ-Casorati Curvatures (δ-CC). We also discuss submanifolds on which the equality situations occur. Lastly, we provided an example derived from this research.

Quasi-Statistical Schouten–van Kampen Connections on the Tangent Bundle

We determine the general natural metrics G on the total space TM of the tangent bundle of a Riemannian manifold (M,g) such that the Schouten–van Kampen connection ∇¯ associated to the Levi-Civita connection of G is (quasi-)statistical. We prove that the base manifold must be a space form and in particular, when G is a natural diagonal metric, (M,g) must be locally flat. We prove that there exist one family of natural diagonal metrics and two families of proper general natural metrics such that (TM,∇¯,G) is a statistical manifold and one family of proper general natural metrics such that (TM∖{0},∇¯,G) is a quasi-statistical manifold.

(ϵ)-Kenmotsu manifold admitting Schouten-van Kampen connection

The objective of this paper is to study some properties of quasi-conformal and concircular tensor on (ϵ)-Kenmotsu manifold admitting the Schouten-van Kampen connection. Expressions of the curvature tensor, Ricci tensor and scalar curvature admitting Schouten-van Kampen connection have been obtained. Locally symmetric (ϵ)-Kenmotsu manifold admitting Schouten-van Kampen connection and quasicon formally flat as well as quasi-conformally semisymmetric (ϵ)-Kenmotsu manifolds admitting Schouten-van Kampen connection are studied.

On Para-Sasakian Manifold with Respect to the Schouten-van Kampen Connection

In the present paper, we have studied the curvature properties of the Schouten-van Kampen connection on the n-dimensional Para Sasakian manifold and obtained some new results. Also, we studied projective curvature tensor, concircular curvature tensor, and Nijenhuis tensor for the Para-Sasakian manifold with respect to the Schouten-van Kampen connection.

Biharmonic Maps on f-Kenmotsu Manifolds with the Schouten–van Kampen Connection

The object of the present paper was to study biharmonic maps on f-Kenmotsu manifolds and f-Kenmotsu manifolds with the Schouten–van Kampen connection. With the help of this connection, our results provided important insights related to harmonic and biharmonic maps.

Geometry of almost contact metrics as a ∗-conformal Ricci–Yamabe solitons and related results

The goal of this paper is to study certain types of metric such as ∗-conformal Ricci–Yamabe soliton (RYS), whose potential vector field is torse-forming on Kenmotsu manifold. Here, we establish the conditions for solitons to be expanding, shrinking or steady and find the scalar curvature when the manifold admits ∗-conformal RYS on Kenmotsu manifold. Next, we developed the nature of the vector field when the manifold satisfies ∗-conformal RYS. Also, we have adorned some applications of torse-forming vector field in terms of ∗-conformal RYS on Kenmotsu manifold. We have also studied infinitesimal CL-transformation and Schouten–van Kampen connection on Kenmotsu manifold, whose metric is ∗-conformal RYS. We present an example of ∗-conformal RYS on three-dimensional Kenmotsu manifold, and verify some of our findings.

$Q$-Curvature Tensor on $f$-Kenmotsu $3$-Manifolds

The object of the present paper is to consider $f$-Kenmotsu $3$-manifolds fulfilling certain curvature conditions on $Q$-curvature tensor with the Schouten-van Kampen connection. Certain consequences of $Q$-curvature tensor on such manifolds bearing Ricci soliton in perspective of Schouten-van Kampen association are likewise displayed. In the last segment, examples are given.

A note on α-cosymplectic manifolds with respect to the Schouten-van Kampen connection

This paper is concerned with some results on α-cosymplectic manifolds admitting the Schouten-van Kampen connection with pseudo-projective and W8-curvature tensor.

Some results on paracontact metric $(k,\mu)$-manifolds with respect to the Schouten-van Kampen connection

In the present paper we study certain symmetry conditions and some types of solitons on paracontact metric $(k,\mu )$-manifolds with respect to the Schouten-van Kampen connection. We prove that a Ricci semisymmetric paracontact metric $(k,\mu )$-manifold with respect to the Schouten-van Kampen connection is an $\eta $-Einstein manifold. We investigate paracontact metric $(k,\mu )$-manifolds satisfying $\breve{Q}\cdot \breve{R}_{cur}=0$\ with respect to the Schouten-van Kampen connection. Also, we show that there does not exist an almost Ricci soliton in a $(2n+1)$-dimensional paracontact metric $(k,\mu )$-manifold with respect to the Schouten-van Kampen connection such that $k>-1$ or $k<-1$. In case of the metric is being an almost gradient Ricci soliton with respect to the Schouten-van Kampen connection, then we state that the manifold is either $N(k)$-paracontact metric manifold or an Einstein manifold. Finally, we present some results related to almost Yamabe solitons in a paracontact metric $(k,\mu )$-manifold equipped with the Schouten-van Kampen connection and construct an example which verifies some of our results.

The Schouten-van Kampen connection on quasi-Sasakian manifolds

"In the present paper, we study three-dimensional quasi-Sasakian manifolds admitting the Schouten-van Kampen connection. We characterize quasi-Sasakian manifolds and nd certain curvature properties with respect to the Schouten-van Kampen connection. Finally, we construct an example of a three-dimensional quasi-Sasakian manifold admitting the Schouten-van Kampen connection which veri es the results discussed in the present paper."

LP-KENMOTSU MANIFOLD ADMITTING SCHOUTEN-VAN KAMPEN CONNECTION

In this paper we study Schouten-van Kampen connection on a Lorentzian para-Kenmotsu manifolds M. We obtain curvature tensor Ř, Ricci tensor Ŝ and scalar curvature ř, with respect to Schouten-van Kampen connection and study their properties. Further, we take some curvature conditions like Ř·Ŝ = 0, Ŝ·Ř = 0 etc., on M and prove Ř·Ć = Ř·Ř. We also consider the cases when M is ξ-concircularly flat, pseudo concircularly flat, φ-concircularly semisymmetric and obtain some interesting results.

On trans-Sasakian 3-manifolds with Da-homotetic deformation with regard to the Schouten-van Kampen connection

We study some soliton types on trans-Sasakian 3-manifolds with Da-homotetic deformation with regard to the Schouten-van Kampen connection.

ON THREE-DIMENSIONAL TRANS-SASAKIAN MANIFOLDS ADMITTING SCHOUTEN-VAN KAMPEN CONNECTION

In the present paper, we study three-dimensional trans-Sasakian manifolds admitting the Schouten-van Kampen connection. Also, we have proved some results on $\phi$-projectively flat, $\xi-$projectively flat and $\xi-$concircularly flat three-dimensional trans-Sasakian manifold with respect to the Schouten-van Kampen connection. Locally $\phi-$symmetry trans-Sasakian manifolds of dimension three have been studied with respect to Schouten-van Kampen connection. Finally, we construct an example of a three-dimensional trans-Sasakian manifold admitting Schouten-van Kampen connection which verifies Theorem 4.1.

SOME CURVATURE PROPERTIES ON PARACONTACT METRIC (k;μ)-MANIFOLDS WITH RESPECT TO THE SCHOUTEN-VAN KAMPEN CONNECTION

The object of the present paper is to characterize paracontact metric (k;μ)-manifolds satisfying certain semisymmetry curvature conditions with respect to the Schouten-van Kampen connection.

On $f$-Kenmotsu manifolds admitting Schouten-Van Kampen connection

In the present paper, we study three-dimensional $f$-Kenmotsu manifolds admitting the Schouten-Van Kampen connection. We study the concircular curvature tensor of a three-dimensional $f$-Kenmotsu manifold with respect to the Schouten-Van Kampen connection. Finally, we have cited an example of a three-dimensional $f$-Kenmotsu manifold admitting Schouten-Van Kampen connection which verify our results.

On f-Kenmotsu 3-manifolds with respect to the Schouten–van Kampen connection

On f-Kenmotsu 3-manifolds with respect to the Schouten–van Kampen connection

On Quasi-Sasakian $3$-Manifolds with Respect to the Schouten-van Kampen Connection

In this paper we study some soliton types on a quasi-Sasakian 3-manifold with respect to the Schouten-van Kampen connection. .............................................. .................................................................................................................................................................................................................................................................................................

LEGENDRE CURVES ON 3-DIMENSIONAL f-KENMOTSU MANIFOLDS ADMITTING SCHOUTEN-VAN KAMPEN CONNECTION

In the present paper, biharmonic Legendre curves with respect to Schouten-Van Kampen connection have been studied on three-dimensional f-Kenmotsu manifolds. Locally $\phi $-symmetric Legendre curves on three-dimensional f-Kenmotsu manifolds with respect to Schouten-Van Kampen Connection have been introduced.Also slant curves have been studied on three-dimensional f-Kenmotsu manifolds with respect to Schouten-Van Kampen connection. Finally, we constract an example of a Legendre curve in a 3-dimensional f-Kenmotsu manifold.

Wintgen inequalities on Legendrian submanifolds of generalized Sasakian-space-forms

A submanifold $M^m$ of a generalized Sasakian-space-form $\overline{M}^{2n+1}(f_1,\allowbreak f_2,f_3)$ is said to be $C$-totally real submanifold if $\xi\in \Gamma(T^\bot M)$ and $\phi X\in \Gamma(T^\bot M)$ for all $X\in \Gamma(TM)$. In particular, if $m=n$, then $M^n$ is called Legendrian submanifold. Here, we derive Wintgen inequalities on Legendrian submanifolds of generalized Sasakian-space-forms with respect to different connections; namely, quarter symmetric metric connection, Schouten-van Kampen connection and Tanaka-Webster connection.