SEMI SYMMETRIC NON-METRIC -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.