Journal of Mathematical Sciences

, Volume 135, Issue 4, pp 3093–3108

Vector fields on n-foliated 2n-dimensional manifolds

  • A. A. Agrachev
  • R. V. Gamkrelidze

DOI: 10.1007/s10958-006-0147-1

Cite this article as:
Agrachev, A.A. & Gamkrelidze, R.V. J Math Sci (2006) 135: 3093. doi:10.1007/s10958-006-0147-1


In this paper, we study basic differential invariants of the pair (vector field, foliation). As a result, we establish a dynamic interpretation and a generalization of the Levi-Civita connection and Riemannian curvature treated as invariants of the geodesic flow on the tangent bundle.

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • A. A. Agrachev
    • 1
  • R. V. Gamkrelidze
    • 2
  1. 1.SISSA-ISAS, Trieste & Steklov Math. Inst.Moscow
  2. 2.Steklov Math. Inst.Moscow