A Note on An Almost Contanct Metric Manifold with A Type of Semi-symmetric Non-metric Connection (original) (raw)

On a semi-symmetric non-metric connection

Filomat, 2012

Yano [1] defined and studied semi-symmetric metric connection in a Riemannian manifold and this was extended by De and Senguta [8] and many other geometers. Recently, the present authors [3], [5] defined semi-symmetric non-metric connections in an almost contact metric manifold. In this paper, we studied some properties of a semi-symmetric non-metric connection in a Kenmotsu manifold.

SEMI SYMMETRIC NON-METRIC S -CONNECTION ON A GENERALIZED CONTACT METRIC STRUCTURE MANIFOLD

In the present paper, we define a semi-symmetric non-metric - connection on a generalized contact metric structure manifold and define the curvature tensor of with respect to semi-symmetric non-metric -connection. It has been shown that if a generalized contact metric structure manifold admits a semi-symmetric non-metric -connection whose curvature tensor is locally isometric to the unit sphere , then the conformal and con-harmonic curvature tensor with respect to Riemannian connection are identical iff . Also it has been shown that if a generalized contact metric structure manifold admits a semi-symmetric non-metric -connection whose curvature tensor is locally isometric to the unit sphere , then the con-circular curvature tensor coincides with curvature tensor with respect to the Riemannian connection if . Some other useful results on projective curvature tensor and con-circular curvature tensor with respect to semi-symmetric non-metric -connection have been obtained.

Connection Adapted to an Almost (Para) Contact Metric Structure

2016

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.

Semi-pseudo symmetric manifolds admitting a semi-symmetric metric connection

2013

In this paper semi-symmetric metric connection have been studied on semi-pseudo Symmetric manifold, and obtained some results when the Ricci tensor of the semi-symmetric metric connection of Codazzi type. Also some restrictions imposed on the curvature tensor and the torsion tensor of the semi-symmetric metric connection and the special conformally flat semi-pseudo symmetric manifold.

Normal complex contact metric manifolds admitting a semi symmetric metric connection

Applied Mathematics and Nonlinear Sciences, 2020

In this paper, we study on normal complex contact metric manifold admitting a semi symmetric metric connection. We obtain curvature properties of a normal complex contact metric manifold admitting a semi symmetric metric connection. We also prove that this type of manifold is not conformal flat, concircular flat, and conharmonic flat. Finally, we examine complex Heisenberg group with the semi symmetric metric connection.

On a Semi Symmetric Metric Connection With a Special Condition On a Riemannian Manifold

European Journal of Pure and Applied Mathematics, 2011

In this study, we consider a manifold equipped with semi symmetric metric connection whose the torsion tensor satisfies a special condition. We investigate some properties of the Ricci tensor and the curvature tensor of this manifold. We obtain a necessary and sufficient condition for the mixed generalized quasi-constant curvature of this manifold. Finally, we prove that if the manifold mentioned above is conformally flat, then it is a mixed generalized quasi-Einstein manifold and we prove that if the sectional curvature of a Riemannian manifold with a semi symmetric metric connection whose the special torsion tensor is independent from orientation chosen, then this manifold is of a mixed generalized quasi constant curvature.