@article{Zubrilin_2013, title={On Preservation of the Order of Flattening by an Induced Diffeomorphism}, volume={65}, url={http://umj.imath.kiev.ua/index.php/umj/article/view/2528}, abstractNote={We consider the structure of a smooth curve from the viewpoint of the concept of flattening and establish conditions under which an <em class="a-plus-plus">r</em>-geodesic curve of the base manifold is the projection of the <em class="a-plus-plus">r</em>-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.}, number={11}, journal={Ukrains’kyi Matematychnyi Zhurnal}, author={ZubrilinK. M.}, year={2013}, month={Nov.}, pages={1482–1497} }