  The sub-Finslerian geometry means that the metric $F$ is defined only on a
given subbundle of the tangent bundle, called a horizontal bundle. In the
paper, a version of the Hopf-Rinow theorem is proved in the case of
sub-Finslerian manifolds, which relates the properties of completeness,
geodesically completeness, and compactness. The sub-Finsler bundle, the
exponential map and the Legendre transformation are deeply involved in this
investigation.

Differential Geometry