Mikeš, Josef; Pokorná, Olga; Starko, Galina On almost geodesic mappings \(\pi_2(e)\) onto Riemannian spaces. (English) Zbl 1050.53021 Slovák, Jan (ed.) et al., The proceedings of the 23th winter school “Geometry and physics”, Srní, Czech Republic, January 18–25, 2003. Palermo: Circolo Matemàtico di Palermo. Suppl. Rend. Circ. Mat. Palermo, II. Ser. 72, 151-157 (2004). A curve \(l\) in an \(n\)-dimensional space \(A_n\) with an affine connection is called almost geodesic if there exists a two-dimensional parallel distribution along \(l\), to which the tangent vector of \(l\) belongs at every point. A diffeomorphism \(f: A_n \to \widetilde{A}_n\) is an almost geodesic mapping if every geodesic of the space \(A_n\) into an almost geodesic curve of the space \(\widetilde{A}_n\). The authors study almost geodesic mappings \(\pi_2(e)\) from the space \(A_n\) onto \(n\)-dimensional Riemannian manifolds \(\widetilde{V}_n\). They refine fundamental equations of almost geodesic mappings \(\pi_2(e):A_n \to \widetilde{A}_n\) and prove that the set of Riemannian manifolds \(\widetilde{V}_n, \, n > 4,\) for which \(A_n\) admits almost geodesic mappings \(\pi_2(e)\), where \(e = -1\), depends on \(\frac{1}{2} n^2 (n+1) + 2n + 3\) real parameters.For the entire collection see [Zbl 1034.53002]. Reviewer: Vladislav V. Goldberg (Newark) Cited in 8 Documents MSC: 53B20 Local Riemannian geometry 53C22 Geodesics in global differential geometry Keywords:Riemannian manifold; almost geodesic mapping; space \(A_n\) with an affine connection PDFBibTeX XMLCite \textit{J. Mikeš} et al., in: The proceedings of the 23rd winter school ``Geometry and physics'', Srní, Czech Republic, January 18--25, 2003. Palermo: Circolo Matemàtico di Palermo. 151--157 (2004; Zbl 1050.53021)