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

Author

Listed:
  • Han Zhang

    (School of Mathematics, Mudanjiang Normal University, Mudanjiang 157011, China
    These authors contributed equally to this work.)

  • Haiming Liu

    (School of Mathematics, Mudanjiang Normal University, Mudanjiang 157011, China
    These authors contributed equally to this work.)

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 .

Suggested Citation

  • Han Zhang & Haiming Liu, 2024. "Sub-Riemannian Geometry of Curves and Surfaces in Roto-Translation Group Associated with Canonical Connection," Mathematics, MDPI, vol. 12(11), pages 1-25, May.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:11:p:1683-:d:1404115
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    References listed on IDEAS

    as
    1. Haiming Liu & Jiajing Miao & Wanzhen Li & Jianyun Guan & Antonio Masiello, 2021. "The Sub-Riemannian Limit of Curvatures for Curves and Surfaces and a Gauss–Bonnet Theorem in the Rototranslation Group," Journal of Mathematics, Hindawi, vol. 2021, pages 1-22, June.
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