  We study some sub-Riemannian objects (such as horizontal connectivity,
horizontal connection, horizontal tangent plane, horizontal mean curvature) in
hypersurfaces of sub-Riemannian manifolds. We prove that if a connected
hypersurface in a contact manifold of dimension more than three is
noncharacteristic or with isolated characteristic points, then given two
points, there exists at least one piecewise smooth horizontal curve in this
hypersurface connecting them. In any sub-Riemannian manifold, we obtain the
sub-Riemannian version of the fundamental theorem of Riemannian geometry. We
use this nonholonomic connection to study horizontal mean curvature of
hypersurfaces.
