  The notions of the interior and truncated connections of a nonholonomic
manifold are introduced. A class of extended truncated connections is
distinguished. For the case of a contact space with a Finsler metric, it is
shown that there exists a unique extended truncated connection that satisfies
additional properties. The curvature tensor of the obtained connection in the
case of a sub-Riemannian space coincides with the Wagner curvature tensor that
was constructed by Wagner for the case of an arbitrary nonholonomic manifold of
codimension one endowed with an interior affine connection.
