By using a statistical connection, we define a semi-symmetric metric connection on statistical manifolds and study the geometry of these manifolds and their submanifolds.We show the symmetry properties of the curvature tensor with respect to the semi-symmetric metric connections.Also, we prove the induced connection on a submanifold with respect to a semi-symmetric metric connection is a semi-symmetric metric connection and the second fundamental form coincides with the second fundamental form of the Levi-Civita connection.Furthermore, we obtain the Gauss, Codazzi and Ricci equations with respect to the new connection.Finally, we construct non-trivial examples of statistical manifolds admitting a semi-symmetric metric connection.
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