The projective quarter symmetric metric connections and reccurent projective curvature tensor

In 1970, Yano, studied Riemannian manifolds admitting semi-symetric metric connections whose curvature tensors vanish. In 1980, Misra and Pardey , studied quarter symmetric metric connections in Riemannian, Kaehlerian and Sasakian manifolds and found some properties of curvature tensors of them. In 1982, Yano and Imai , gave the most general form of quarter symetric metric connections and studied its applications. In 2008, Zhao, investigated the properties of projective semi-symmetric metric connections of a Riemannian manifold and gave some interesting results with respect to this semi -symmetric connection. In the present paper, after describing the projective quarter symmetric metric connection D, we define a projective recurrent manifold M with respect to D and study some properties of it.