  In this paper, we define deformed Schouten-Van Kampen connections which are
metric connections and compute sub-Riemannian limits of Gaussian curvature for
a Euclidean C2-smooth surface associated to deformed Schouten-Van Kampen
connections with two kinds of distributions in the affine group and the group
of rigid motions of the Minkowski plane away from characteristic points and
signed geodesic curvature for Euclidean C2-smooth curves on surfaces. According
to above results, we get Gauss-Bonnet theorems associated to two kinds of
deformed Schouten-Van Kampen connections in the affine group and the group of
rigid motions of the Minkowski plane.
