On (m¯, m)-Conformal Mappings

Conformal mappings between Riemannian spaces R¯N and RN are defined by the explicit transformation of the metric tensor of the space R¯N to the metric tensor of the space RN. Geodesic mapping between these two Riemannian spaces is a transformation that transforms any geodesic line of the space R¯N to a geodesic line of the space RN. In this research, we defined an m-conformal line of a Riemannian space, which is geodesic if m=0. Based on this definition, we involved the concept of (m¯,m)-conformal mapping as a transformation R¯N→RN in which any m¯-conformal line of the space R¯N transforms to an m-conformal line of the space RN. The result of this research is the establishment of three invariants for these mappings. At the end of this research, we gave an example of a scalar geometrical object which may be used in physics.