Weingarten Surfaces with moving frames - A tribute to S. S. Chern and C. L. Terng - And a Duality result

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Abstract

The techniques used, in this paper, are based on the exterior calculus of Maurer-Cartan forms, and Weingarten surfaces are used to illustrate the methods that apply to quadratic exterior equations with constant coefficients. Isothermic surfaces of constant astigmatism (non-linear Weingarten surfaces whose difference of principal curvatures is a constant) are shown to represent dual surfaces of isothermic surfaces which satisfy the relation H + αK = 0.

Original languageEnglish
Pages (from-to)263-289
Number of pages27
JournalJP Journal of Geometry and Topology
Volume12
Issue number3
StatePublished - Nov 2012

Keywords

  • Cartan's moving frame method
  • Dual surfaces
  • Isothermic coordinates
  • Linear weingarten surface
  • Weingarten surface

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