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.

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.