Sub-Riemannian Geometry of Curves and Surfaces in Roto-Translation Group Associated with Canonical Connection.

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 . [ABSTRACT FROM AUTHOR]