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

Abstract

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.

It has been accepted for publication in SCIENCE CHINA Mathematics

References in corpus (1)

• Rotation surfaces of constant Gaussian curvature as Riemannian approximation scheme in sub-Riemannian Heisenberg space ${\mathbb{H}}^1$

Cited by in corpus (2)

• Limit of Gaussian and normal curvatures of surfaces in Riemannian approximation scheme for sub-Riemannian three dimensional manifolds and Gauss-Bonnet theorem
• Affine connections and Gauss-Bonnet theorems in the Heisenberg group