Geodesic mappings onto generalized m-Ricci-symmetric spaces

Abstract

In this paper, we study geodesic mappings of spaces with affine connections onto generalized 2-, 3-, and m-Ricci-symmetric spaces. In either case, the main equations for the mappings are obtained as a closed system of linear differential equations of the Cauchy type in the covariant derivatives. For the systems, we have found the maximum number of essential parameters on which the solutions depend. These results generalize the properties of geodesic mappings onto symmetric, recurrent, and also 2-, 3-, and m-(Ricci-)symmetric spaces with affine connections.In this paper, we study geodesic mappings of spaces with affine connections onto generalized 2-, 3-, and m-Ricci-symmetric spaces. In either case, the main equations for the mappings are obtained as a closed system of linear differential equations of the Cauchy type in the covariant derivatives. For the systems, we have found the maximum number of essential parameters on which the solutions depend. These results generalize the properties of geodesic mappings onto symmetric, recurrent, and also 2-, 3-, and m-(Ricci-)symmetric spaces with affine connections.