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

Han Zhang and Haiming Liu ()
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Han Zhang: School of Mathematics, Mudanjiang Normal University, Mudanjiang 157011, China
Haiming Liu: School of Mathematics, Mudanjiang Normal University, Mudanjiang 157011, China

Mathematics, 2024, vol. 12, issue 11, 1-25

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 .

Keywords: sub-Riemannian; canonical connection; Gauss-Bonnet theorem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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