Geodesic mappings of manifolds with affine connection onto the Ricci symmetric manifolds

Abstract

In the present paper we investigate geodesic mappings of manifolds with affine connection onto Ricci symmetric manifolds which are characterized by the covariantly constant Ricci tensor. We obtained a fundamental system for this problem in a form of a system of Cauchy type equations in covariant derivatives depending on no more than n(n + 1) real parameters. Analogous results are obtained for geodesic mappings of manifolds with afine connection onto symmetric manifolds.

Geodesic mappings of spaces with affine connnection onto generalized Ricci symmetric spaces

“…From the conditions (1) and (2) it follows that the spaceĀ n from the Theorem 3.1 has the equiaffine connection…”

“…We obtained [1,2] that fundamental equations of geodesic mappings of spaces with affine connection onto Riemannian spaces and fundamental equations of geodesic mappings of spaces with affine connection onto Ricci symmetric spaces are formed to closed Cauchy type equations system in covariant derivative. Moreover, for geodesic mappings onto Riemannian spaces this system is linear.…”

“…Let us note, that generalized Ricci symmetric space which is (pseudo-) Riemannian space is Ricci symmetric (R ij|k = 0). Let us remark, that the geodesic mappings of Ricci symmetric spaces were studied in [1].…”

“…Geodesic mappings onto Ricci symmetric manifolds were studied in [1]. In our case the equations of such mapping would be simpler becauseĀ n is equiaffine.…”

“…Geodesic mappings of Einstein, symmetric, recurrent spaces and the generalizations of these mappings were studied in [1, 2, 8, 10, 13, 16-22, 26-29, 31, 33, 36, 39, 41]. Detailed analysis of geodesic mappings of generalized symmetric recurrent manifolds is presented in work [1,3].…”