SUBMANIFOLDS OF A RIEMANNIAN MANIFOLD ADMITTING A TYPE OF RICCI QUARTER-SYMMETRIC METRIC CONNECTION
Abstract
The object 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 quartersymmetric
metric connection. We have also consider the mean curvature and
the shape operator of 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 manifold and its submanifold with respect to the
Ricci quarter-symmetric metric connection.
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