Generalized Weyl conformal curvature tensor of generalized Riemannian space

Abstract

It is generalized Weyl conformal curvature tensor in the case of a conformal mappings of a generalized Riemannian space in this paper. Moreover, it is found universal generalizations of it without any additional assumption. A method used in this paper may help different scientists in their researching. Many research papers, books and monographs are dedicated to development of the theory of conformal mappings and its applications. Some of authors who have contributed to this development are H. M. Abood [1], S. Bochner [2], L. P. Eisenhart [8], S. B. Mathur [11], Josef Mikeš with his research group [3, 4, 9, 12-14, 18, 24], S. M. Minčić [21], P. Mocanu [17], M. Prvanović [19], N. S. Sinyukov [20], M. Lj. Zlatanović, M. Najdanović [18, 24] and many others. A. Einstein [5-7] based the theory of general relativity on non-symmetric affine connection. E. Goulart and M. Novello [10] such as H. Zhang, Y. Zhang, X-Z. Li [23] applied the theory of conformal mappings in physics.The main purpose of this paper is to make analogies between invariants of geodesic and conformal mappings, i.e. we want to examine are there analogies of Thomas projective parameter and Weyl projective tensor as invariants of conformal mappings in here.