The Sub-Riemannian Limit of Curvatures for Curves and Surfaces and a Gauss-Bonnet Theorem in the Rototranslation Group

被引：8

作者：

Liu, Haiming ^{[1
]}

Miao, Jiajing ^{[1
]}

Li, Wanzhen ^{[1
]}

Guan, Jianyun ^{[1
]}

机构：

[1] Mudanjiang Normal Univ, Sch Math, Mudanjiang 157011, Peoples R China

来源：

JOURNAL OF MATHEMATICS | 2021年 / 2021卷

关键词：

D O I：

10.1155/2021/9981442

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The rototranslation group RJ is the group comprising rotations and translations of the Euclidean plane which is a 3-dimensional Lie group. In this paper, we use the Riemannian approximation scheme to compute sub-Riemannian limits of the Gaussian curvature for a Euclidean C-2-smooth surface in the rototranslation group away from characteristic points and signed geodesic curvature for Euclidean C-2-smooth curves on surfaces. Based on these results, we obtain a Gauss-Bonnet theorem in the rototranslation group.

引用

页数：22

共 33 条

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