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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].

MSC:

53B20 Local Riemannian geometry
53C22 Geodesics in global differential geometry
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