SUBMANIFOLDS OF A RIEMANNIAN MANIFOLD ADMITTING A TYPE OF RICCI QUARTER-SYMMETRIC METRIC CONNECTION

The aim of the present paper is to study submanifolds of a Riemannian manifold admitting a type of Ricci quater-symmetric metric connection. We have proved that the induced connection is also a Ricci quarter-symmetric metric connection. We have also considered the mean curvature and the shape operator of the submanifold with respect to the Ricci quarter-symmetric metric connection. We have obtained the Gauss, Codazzi and Ricci equations with respect to the Ricci quarter-symmetric metric connection. Finally, we have considered the totally geodesicness and obtained the relation between the sectional curvatures of the manifold and its submanifold with respect to the Ricci quarter-symmetric metric connection.