Weingarten surfaces with moving frames -- a tribute to S.S. Chern and C.L. Terng -- and a duality result

Magdalena Toda

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arXiv · 1302.5395

Weingarten surfaces with moving frames -- a tribute to S.S. Chern and C.L. Terng -- and a duality result

Magdalena Toda

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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 {\it 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 $H + \alpha K = 0$.

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Magdalena Toda. 2013-02-21. Weingarten surfaces with moving frames -- a tribute to S.S. Chern and C.L. Terng -- and a duality result. https://arxiv.org/abs/1302.5395

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