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

Magdalena Toda

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

Magdalena Toda

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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 language	English
Pages (from-to)	263-289
Number of pages	27
Journal	JP Journal of Geometry and Topology
Volume	12
Issue number	3
State	Published - Nov 2012

Keywords

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

Cite this

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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.",

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N2 - 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.

AB - 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.

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KW - Isothermic coordinates

KW - Linear weingarten surface

KW - Weingarten surface

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

Abstract

Keywords

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