Diffeomorphism of affine connected spaces which preserved Riemannian and Ricci curvature tensors

Abstract

In the present paper we study the preserving of Riemannian and Ricci tensors with respect to a diffeomorphism of spaces with affine connection. We consider geodesic and almost geodesic mappings of the first type. The basic equations of these maps form a closed system of Cauchy type in covariant derivatives. We determine the quantity of essential (substantial) parameters, on which depend the general solution of this problem.