Ukrainian Mathematical Journal

, Volume 65, Issue 11, pp 1642–1660 | Cite as

On Preservation of the Order of Flattening by an Induced Diffeomorphism

  • K. M. Zubrilin

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.


Boundary Point Tangent Bundle Parametric Equation Geodesic Curve Base Manifold 
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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • K. M. Zubrilin
    • 1
  1. 1.Feodosiya Polytechnic Institute of the Admiral Makarov National University of ShipbuildingFeodosiyaUkraine

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