We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Sub-Riemannian Geometry of Curves and Surfaces in Roto-Translation Group Associated with Canonical Connection.
- Authors
Zhang, Han; Liu, Haiming
- Abstract
The aim of this paper is to obtain the sub-Riemannian properties of the roto-translation group R T . At the same time, we compute the sub-Riemannian limits of Gaussian curvature associated with two kinds of canonical connections for a C 2 -smooth surface in the roto-translation group away from characteristic points and signed geodesic curvature associated with two kinds of canonical connections for C 2 -smooth curves on surfaces. Based on these results, we obtain a Gauss-Bonnet theorem in the R T .
- Subjects
SURFACE geometry; GAUSS-Bonnet theorem; GEOMETRIC surfaces; GAUSSIAN curvature; GEODESICS; RIEMANNIAN geometry; CURVATURE
- Publication
Mathematics (2227-7390), 2024, Vol 12, Issue 11, p1683
- ISSN
2227-7390
- Publication type
Article
- DOI
10.3390/math12111683