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

2019/12/01 by Yong Wang, Wang, Yong, Sining Wei +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1912.00302

openalex publication_date 2019/12/01 · openalex created_date 2019/12/05 · openalex updated_date 2026/07/28

Abstract

In this paper, we compute sub-Riemannian limits of Gaussian curvature for a Euclidean C²-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 C²-smooth curves on surfaces. We get Gauss-Bonnet theorems in the affine group and the group of rigid motions of the Minkowski plane.

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