Kampen Connection Research Articles

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.

Some curvature proprieties of Kenmotsu manifolds with the Schouten-van Kampen connection

Some curvature proprieties of Kenmotsu manifolds with the Schouten-van Kampen connection

Study on generalised pseudo (Ricci) symmetric Sasakian manifold admitting general connection

The object of the present paper is to study the generalized pseudo (Ricci) symmetric Sasakian manifold with respect to a new connection named general connection. The general connection has the flavor of the quarter-symmetric connection, generalized Tanaka-Webster connection, Zamkovoy, and Schouten- van Kampen connection. The existence of generalized pseudo (Ricci) symmetric Sasakian manifold with respect to general connection is ensured by an example.

Some curvature proprieties of Kenmotsu manifolds with the Schouten-van Kampen connection

The aim of the present paper is to study the concircular curvature tensor, projective curvature tensor, Weyl conformal curvature tensor of Kenmotsu manifolds admitting Schouten-van Kampen connection and an example is given to verify our results.

On Quasi-Sasakian Manifolds

In this paper we study three-dimensional quasi-Sasakian manifolds admitting the Schouten-van Kampen connection. Also, we study D-homothetic deformations on three-dimensional quasi-Sasakian manifolds admitting Schouten-van connection and projectively flat three-dimensional quasi-Sasakian manifolds admitting scv connection.

Kenmotsu manifolds admitting Schouten-Van Kampen Connection

The objective of the present paper is to study Kenmotsu manifold admitting Schouten-van Kampen connection. We study Kenmotsu manifold admitting Schouten-van Kampen connection satisifying certain curvature conditions. Also we prove equivalent conditions for Ricci soliton in a Kenmotsu manifold is steady with respect to the Schouten-van Kampen connection.

On Schouten-van Kampen connection in Sasakian manifolds

We study the Schouten-van Kampen connection associated to a Sasakian structure. With the help of the Schouten-van Kampen connection we characterize Sasakian manifolds and find certain curvature properties of this connection on Sasakian manifolds. Also we study Ricci solitons on a Sasakian manifold with respect to the Schouten-van Kampen connection. Finally, an illustrative example is given to verify some results.

The Schouten–Van Kampen connection on the (1, 1)-tensor bundle

The problems in the present paper are related to the Schouten–Van Kampen connection $$\overline{\nabla }$$ associated with the Levi-Civita connection $$\widetilde{\nabla }$$ of the Riemannian metric $$\widetilde{g}$$ which includes both Sasaki and Cheeger–Gromoll type metrics on the (1, 1)-tensor bundle. Firstly, we define the Schouten–Van Kampen connection $$\overline{\nabla }$$ on the (1, 1)-tensor bundle and give some applications concerning $$\overline{\nabla }$$ . Secondly, we compute all forms of curvature tensors of $$\overline{\nabla }$$ . Thirdly, we consider an almost product structure which is compatible with the Riemannian metric $$\widetilde{g}$$ and investigate the conditions under which this structure is parallel with respect to $$\overline{\nabla }$$ . Lastly, we define and study the deformation algebra of the connections $$(\overline{\nabla },\widetilde{\nabla })$$ .

On metric connections with torsion on the cotangent bundle with modified Riemannian extension

Let M be an n-dimensional differentiable manifold equipped with a torsion-free linear connection $$\nabla $$ and $$T^{*}M$$ its cotangent bundle. The present paper aims to study a metric connection $$\widetilde{ \nabla }$$ with nonvanishing torsion on $$T^{*}M$$ with modified Riemannian extension $${}\overline{g}_{\nabla ,c}$$ . First, we give a characterization of fibre-preserving projective vector fields on $$(T^{*}M,{}\overline{g} _{\nabla ,c})$$ with respect to the metric connection $$\widetilde{\nabla }$$ . Secondly, we study conditions for $$(T^{*}M,{}\overline{g}_{\nabla ,c})$$ to be semi-symmetric, Ricci semi-symmetric, $$\widetilde{Z}$$ semi-symmetric or locally conharmonically flat with respect to the metric connection $$ \widetilde{\nabla }$$ . Finally, we present some results concerning the Schouten–Van Kampen connection associated to the Levi-Civita connection $$ \overline{\nabla }$$ of the modified Riemannian extension $$\overline{g} _{\nabla ,c}$$ .

Dimensional -Kenmotsu Manifolds with Respect to Schouten-van Kampen Connection

Dimensional -Kenmotsu Manifolds with Respect to Schouten-van Kampen Connection

F-Kenmotsu manifolds with the Schouten-van Kampen connection

We study 3-dimensional f-Kenmotsu manifolds with the Schouten-van Kampen connection. With the help of such a connection, we study projectively flat, conharmonically flat, Ricci semisymmetric and semisymmetric 3-dimensional f-Kenmotsu manifolds. Finally, we give an example of 3- dimensional f-Kenmotsu manifolds with the Schouten-van Kampen connection.

The Schouten-van Kampen affine connection adapted to an almost (para) contact metric structure

We study the Schouten-van Kampen connection associated to an almost contact or paracontact metric structure. With the help of such a connection, some classes of almost (para) contact metric manifolds are characterized. Certain curvature properties of this connection are found.