On Preservation of the Order of Flattening by an Induced Diffeomorphism
We consider the structure of a smooth curve from the viewpoint of the concept of flattening and establish conditions under which an r-geodesic curve of the base manifold is the projection of the r-geodesic curve in a tangent bundle of the second order. The necessary and sufficient condition under which a 2-geodesic diffeomorphism of affine-connected spaces induces a 2-geodesic diffeomorphism of tangent bundles of the second order is established.
English version (Springer): Ukrainian Mathematical Journal 65 (2013), no. 11, pp 1642-1660.
Citation Example: Zubrilin K. M. On Preservation of the Order of Flattening by an Induced Diffeomorphism // Ukr. Mat. Zh. - 2013. - 65, № 11. - pp. 1482–1497.