On Canonical Almost Geodesic Mappings of Type π2(e)

Abstract

For modelling of various physical processes, geodesic lines and almost geodesic curves serve as a useful tool. Trasformations or mappings between spaces (endowed with the metric or connection) which preserve such curves play an important role in physics, particularly in mechanics, and in geometry as well. Our aim is to continue investigations concerning existence of almost geodesic mappings of manifolds with linear (affine) connection, particularly of the so-calledπ 1 mappings, i.e. canonical almost geodesic mappings of type π 1 according to Sinyukov. First we give necessary and sufficient conditions for existence ofπ 1 mappings of a manifold endowed with a linear connection onto pseudo-Riemannian manifolds. The conditions take the form of a closed system of PDE's of first order of Cauchy type. Further we deduce necessary and sufficient conditions for existence ofπ 1 mappings onto generalized Ricci-symmetric spaces. Our results are generalizations of some previous theorems obtained by N.S. Sinyukov.

Novel invariants for almost geodesic mappings of the third type

“…Mapping f : A N → A N is an almost geodesic mapping if any geodesic line of A N transforms to an almost geodesic line in A N see [2,3,5,14,15] .…”

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

“…In paper [3], see [26, pp. 469-473], we studied geodesic mappings onto generalized Ricci symmetric space.…”

“…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].…”

Canonical Almost Geodesic Mappings of the First Type of Spaces with Affine Connections onto Generalized m-Ricci-Symmetric Spaces

“…Sobchuk [19,20], N.Y. Yablonskaya [21,22], V.E. Berezovski, J. Mikeš [14,15,[23][24][25][26][27][28][29][30][31][32][33][34][35], O. Belova, J. Mikeš, K. Strambach [36,37], M.S. Stankovič, Lj.S.…”