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 |
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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