Projective Curvature Tensors of Some Special Manifolds with Non-symmetric Linear Connection

Abstract

We consider geodesic mappings between some special manifolds with the non-symmetric linear connection. We obtain some tensors that are invariant with respect to geodesic mappings by relaxing the so-called “equitorsion condition”. Derived tensors have algebraic expressions analogous to the Weyl tensor of projective curvature, apart from that the generalized Ricci and curvature tensors appeared instead of the usual Ricci and curvature tensors. Further, we study some properties of mentioned invariant tensors as well as their relations with the Weyl tensor of projective curvature. Finally, we introduce some kinds of recurrent manifolds with the non-symmetric linear connection as well as their generalized Ricci and projective counterparts.