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Darboux curves on surfaces II

  • Ronaldo GarciaEmail author
  • Rémi Langevin
  • Paweł Walczak
Article
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Abstract

In 1872, Gaston Darboux defined a family of curves on surfaces in the 3-dimensional Euclidean space E3 which are preserved by the action of the Möbius group and share many properties with geodesics. Here, we study the Darboux curves from a dynamical viewpoint on special canal surfaces, quadrics and some Darboux cyclides. We also describe the generic behavior of Darboux curves near ridge points (zig-zag and beak-to-beak).

Keywords

Darboux curves conformal geometry space of spheres canal surfaces ridge points 

Mathematical subject classification

53A30 53C12 53C50 57R30 

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Copyright information

© Sociedade Brasileira de Matemática 2016

Authors and Affiliations

  • Ronaldo Garcia
    • 1
    Email author
  • Rémi Langevin
    • 2
  • Paweł Walczak
    • 3
  1. 1.Instituto de Matemática e EstatísticaUniversidade Federal de GoiásGoiâniaBrazil
  2. 2.Institut de Mathématiques de Bourgogne, UMR CNRS 5584, U.F.R. Sciences et TechniquesUniversité de Bourgogne-Franche-ComtéDIJON CedexFrance
  3. 3.Katedra Geometrii, Wydział Matematyki i InformatykiUniwersytet ŁódzkiŁódźPoland

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