Abstract
In this paper, we consider conformal mappings of Riemannian spaces onto Ricci-2-symmetric Riemannian spaces and geodesic mappings of spaces with affine connections onto Ricci-2-symmetric spaces. The main equations for the mappings are obtained as a closed system of Cauchy-type differential equations in covariant derivatives. We find the number of essential parameters which the solution of the system depends on. A similar approach was applied for the case of conformal mappings of Riemannian spaces onto Ricci-m-symmetric Riemannian spaces, as well as geodesic mappings of spaces with affine connections onto Ricci-m-symmetric spaces.
Highlights
Conformal mappings have been considered in many monographs, surveys, and papers
Sinyukov [16] has proved that the main equations for geodesic mappings ofRiemannian spaces are equivalent to some linear system of Cauchy-type differential equations in covariant derivatives
In the paper [19], the authors proved that the main equations of geodesic mappings of spaces with affine connections onto Ricci-symmetric spaces were equivalent to some system of Cauchy-type differential equations in covariant derivatives
Summary
Conformal mappings have been considered in many monographs, surveys, and papers. Sinyukov [16] has proved that the main equations for geodesic mappings of (pseudo-)Riemannian spaces are equivalent to some linear system of Cauchy-type differential equations in covariant derivatives. In the paper [19], the authors proved that the main equations of geodesic mappings of spaces with affine connections onto Ricci-symmetric spaces were equivalent to some system of Cauchy-type differential equations in covariant derivatives. The main equations for conformal mappings of Riemannian spaces onto Ricci-2-symmetric Riemannian spaces and geodesic mappings of spaces with affine connections onto Ricci-2-symmetric spaces are obtained as closed-system. We find the number of essential parameters which the solution of the system depends on, and the obtained results are extended for the case of conformal mappings of Riemannian spaces onto Ricci-m-symmetric Riemannian spaces and geodesic mappings of spaces with affine connections onto Ricci-m-symmetric spaces. Throughout the paper, that all geometric objects under consideration are continuous and sufficiently smooth
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