Gauss-Bonnet theorems in the affine group and the group of rigid motions of the Minkowski plane

摘要

In this paper,we compute sub-Riemannian limits of Gaussian curvature for a Euclidean C^(2)-smooth surface in the affine group and the group of rigid motions of the Minkowski plane away from characteristic points and signed geodesic curvature for Euclidean C^(2)-smooth curves on surfaces.We get Gauss-Bonnet theorems in the affine group and the group of rigid motions of the Minkowski plane.