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. general case of a geodesic mapping f of two non-symmetric affine connection spaces G A N and G A ¯ N , it is impossible to obtain a generalization of the Weyl projective curvature tensor. In the present paper, we study the case when G A N and G A ¯ N have the same torsion at corresponding points. We name such a mapping “equitorsion mapping”. In the work Stanković (2010) [19] we obtained quantities E θ j m n i ( θ = 1 , … , 5 ) , that are generalizations of the Weyl tensor, i.e. they are invariants based on f . Among E θ only E 5 is a tensor. the another 5 linearly independent curvature tensors, we proved that there exist 3 equitorsion projective tensors.