On Preservation of the Order of Flattening by an Induced Diffeomorphism

  • K. M. Zubrilin

Abstract

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.
Published
25.11.2013
How to Cite
ZubrilinK. M. “On Preservation of the Order of Flattening by an Induced Diffeomorphism”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 65, no. 11, Nov. 2013, pp. 1482–1497, http://umj.imath.kiev.ua/index.php/umj/article/view/2528.
Section
Research articles