Affiliation:
1. School of Mathematics, Mudanjiang Normal University, Mudanjiang 157011, China
Abstract
The aim of this paper is to obtain the sub-Riemannian properties of the roto-translation group RT. At the same time, we compute the sub-Riemannian limits of Gaussian curvature associated with two kinds of canonical connections for a C2-smooth surface in the roto-translation group away from characteristic points and signed geodesic curvature associated with two kinds of canonical connections for C2-smooth curves on surfaces. Based on these results, we obtain a Gauss-Bonnet theorem in the RT.
Funder
the Project of Science and Technology of Heilongjiang Provincial Education Department
the Reform and Development Foundation for Local Colleges and Universities of the Central Government
Project of KCSZ of MNU
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