The Sub-Riemannian Limit of Curvatures for Curves and Surfaces and a Gauss–Bonnet Theorem in the Rototranslation Group
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 rot...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2021-01-01
|
| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/9981442 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | 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. |
|---|---|
| ISSN: | 2314-4629 2314-4785 |