  In this paper, we study the doubly warped product manifolds with
semisymmetric metric connection. We derive the curvatures formulas for doubly
warped product manifold with semi-symmetric metric connection in terms of
curvatures of components of doubly warped product manifolds. We also prove the
necessary and sufficient condition for a doubly warped product manifold to be a
warped product manifold. We obtain some results for Einstein doubly warped
product manifold and Einstein-like doubly warped product manifold of class A
with respect to a semi-symmetric metric connection.
