Non-special, non-canal isothermic tori with spherical lines of curvature

Bernstein, Holly

doi:10.1090/S0002-9947-00-02691-X

Non-special, non-canal isothermic tori with spherical lines of curvature
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Trans. Amer. Math. Soc. 353 (2001), 2245-2274 Request permission

Abstract:

This article examines isothermic surfaces smoothly immersed in Möbius space. It finds explicit examples of non-special, non-canal isothermic tori with spherical lines of curvature in two systems by analyzing Darboux transforms of Dupin tori. In addition, it characterizes the property of spherical lines of curvature in terms of differential equations on the Calapso potential of the isothermic immersion, and investigates the effect of classical transformations on this property.

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