New projective tensors for equitorsion geodesic mappings

In this paper, we consider the manifolds with non-symmetric connection. Using the non-symmetric affine connection and four kinds of differentiation, 5 independent curvature tensors Minčić (1979) [17] appear. In the general case of a geodesic mapping f of two non-symmetric affine connection spaces GAN and GA¯N, it is impossible to obtain a generalization of the Weyl projective curvature tensor. In the present paper, we study the case when GAN and GA¯N have the same torsion at corresponding points. We name such a mapping “equitorsion mapping”. In the work Stanković (2010) [19] we obtained quantities Eθjmni(θ=1,…,5), that are generalizations of the Weyl tensor, i.e. they are invariants based on f. Among Eθ only E5 is a tensor. Using the another 5 linearly independent curvature tensors, we proved that there exist 3 equitorsion projective tensors.