  In this paper, we compute sub-Riemannian limits of Gaussian curvature
associated to two kinds of Schouten-Van Kampen affine connections and the
adapted connection for a Euclidean $C^2$-smooth surface in the Heisenberg group
away from characteristic points and signed geodesic curvature associated to two
kinds of Schouten-Van Kampen affine connections and the adapted connection for
Euclidean $C^2$-smooth curves on surfaces. We get Gauss-Bonnet theorems
associated to two kinds of Schouten-Van Kampen affine connections in the
Heisenberg group.
