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Considering a non-symmetric linear connection and its dual one appear 6 independent curvature tensors [15]. In the present paper we study properties of curvature tensors of semi-symmetric metric connections on a generalized Riemannian manifold. It is shown that if linear connection preserves the symmetric part of the generalized Riemannian metric with semi-symmetric torsion with an appropriate additional condition, then these six curvature tensors can be expressed by linear combination of Weyl conformal curvature tensor, Weyl projective curvature tensor and the concircular curvature tensor. In the case of the curvature tensor   , we have proved that if exists a linear connection preserving the symmetric part of the generalized Riemannian metric with semi-symmetric torsion, whose curvature tensor    vanishes, it is necessary and sucient that the Riemannian metric be projectively flat. For tensor    we also get a useful result. If exists a linear connection    preserving the symmetric part of the generalized Riemannian metric with semi-symmetric torsion, whose curvature tensor    and Ricci tensor    vanish, it is necessary and sucient that the Riemannian metric be conformally flat.

Curvature properties of metric and semi-symmetric linear connections