On equitorsion geodesic mappings of general affine connection spaces
Summary: In the papers [the second author, Mat. Vesn. 10, No. 25, 161--172 (1973; Zbl 0278.53012); Publ. Inst. Math., Nouv. Sér. 22, No. 36, 189--199 (1977; Zbl 0377.53008)], several Ricci type identities are obtained by using a non-symmetric affine connection. In these identities appear 12 curvature tensors, 5 of which being independent, while the rest can be expressed as linear combinations of the others. In the general case of a geodesic mapping \(f\) of two non-symmetric affine connection spaces \(GA_N\) and \(G\bar{A}_N\) it is impossible to obtain a generalization of the Weyl projective curvature tensor. In the present paper, we study the case when \(GA_N\) and \(G\bar{A}_N\) have the same torsion in corresponding points. Such a mapping we name ``equitorsion mapping''. With respect to each of the curvature tensors mentioned above, we obtain quantities \(\mathop\mathcal{E}_{\theta^{jmn}}^i\) \((\theta = 1,\ldots,5)\), that are generalizations of the Weyl tensor, i.e., they are invariants based on \(f\) . Among \(\mathop\mathcal{E}\limits_{\theta}\) only \(\mathop\mathcal{E}\limits_{5}\) is a tensor. All these quantities are interesting for constructions of new mathematical and physical structures.
scientific article; zbMATH DE number 5849496
scientific article