  The authors first in this paper define a semi-symmetric metric non-holonomic
connection (called in briefly a semi-sub-Riemannian connection) on
sub-Riemannian manifolds, and study the relations between sub-Riemannian
connections and semi-sub-Riemannian connections. An invariant under a
connection transformation $\nabla\rightarrow D$ is obtained. The authors then
further deduce a sufficient and necessary condition that a sub-Riemannian
manifold associated with a semi-sub-Riemannian connection is flat, and derive
that a sub-Riemannian manifold with vanishing curvature with respect to
semi-sub-Riemannnian connection $D$ is a group manifold if and only if it is of
constant curvature.
