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

Haiming Liu, Jiajing Miao, Wanzhen Li, Jianyun Guan and Antonio Masiello

Journal of Mathematics, 2021, vol. 2021, 1-22

Abstract: The rototranslation group ℛT 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 C2-smooth surface in the rototranslation group away from characteristic points and signed geodesic curvature for Euclidean C2-smooth curves on surfaces. Based on these results, we obtain a Gauss–Bonnet theorem in the rototranslation group.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:9981442

DOI: 10.1155/2021/9981442

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