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We studied rules of transformations of Christoffel symbols under third type almost geodesic mappings in this paper. From this research, we obtained some new invariants of these mappings. These invariants are analogies of Thomas projective parameter and Weyl projective tensor.

This study is motivated by the researches in the field for invariants of geodesic and conformal mappings presented in T. Y. Thomas, [17] and H. Weyl,[20] . The Thomas projective parameter and the Weyl projective tensor are generalized in this article. Generators for vector spaces of invariants of geometric mappings are obtained in here.

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Vanishing of linearly independent curvature tensors of a non-symmetric affine connection space as functions of vanished curvature tensor of the associated space of this one are analyzed in the first part of this paper. Projective curvature tensors of a non-symmetric affine connection space are expressed as functions of the affine connection coefficients and Weyl projective tensor of the corresponding associated affine connection space in the second part of this paper.