The authors firstly in this paper define a semi-symmetric metric non-holonomic connection (in briefly, SS-connection) on sub-Riemannian manifolds. An invariant under a SS-connection transformation is obtained. The authors then further give a result that a sub-Riemannian manifold (M,V0,g,∇¯)(M,V0,g,∇¯) is locally horizontally flat if and only if MM is horizontally conformally flat and horizontally Ricci flat.
