Some Curvature Properties on a Generalized Contact Metric Structure Manifold

Abstract

In the present paper, We have defined generalized contact metric structure manifold admitting semi-symmetric metric S -connection and the form of curvature tensor R of the manifold relative to this connection has been derived. It has been shown that if a generalized contact metric manifold admits a semi-symmetric metric S -connection whose curvature tensor is locally isometric to the unit sphere Sn(1) , then the con-harmonic and conformal curvature tensors with respect to the Riemannian connection are identical iff 2a2 n 0 c + = . Under the same condition it has been shown that con-circular curvature tensor C coincides with the curvature tensor K with respect to Riemannian connection.