On Special First-Type Almost Geodesic Mappings of Affine Connection Spaces Preserving a Certain Tensor

摘要

In the sixties, Sinyukov [1] introduced almost geodesics mappings of Riemannian and affinely connected spaces; the main related results are presented in the monograph [2] and the surveys [3] and[4]. The theory of almost geodesies mappings was developed in a natural way by many authors; see, e.g. [5]-[15]. Almost geodesies mappings of the first type, distinguished by Sinyukov, were studied by Berezovskii and Mikes [7]-[10] and by Yablonskaya[16]. This study implements, in particular, Petrov's program of modeling physical processes by using mappings and transformations outlined in[17]. This paper considers special cases of first-type canonical almost geodesies mappings of spaces with affine connection. The basic equations of the mappings under consideration are reduced to a Cauchy-type closed system of covariant differential equations. The number of essential parameters on which the general solution depends is determined. An example of a class of such mappings is given.