## 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