On submanifolds of a Riemannian manifold with a semi-symmetric non-metric connection

Under investigation were the submanifolds of a Riemannian manifold with a semi-symmetric non-metric connection. We have proved that the induced connection is also a semi-symmetric non-metric connection. The totaly geodesicness and the minimality of a submanifold of a Riemannian manifold with a semi-symmetric non-metric connection were also considered. We have obtained the Gauss, Codazzi and Ricci equations with respect to a semi-symmetric, non-metric connection. The relation between the sectional curvatures of the Levi-Civita connection and the semi-symmetric non-metric connection is also obtained.