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

Author(s): Holly Bernstein
Journal: Trans. Amer. Math. Soc. 353 (2001), 2245-2274.
MSC (1991): Primary 53A05; Secondary 51B10, 58G37
Posted: November 28, 2000
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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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Additional Information:

Holly Bernstein
Affiliation: Department of Mathematics, Washington University in St. Louis, Campus Box 1146, One Brookings Drive, St. Louis, Missouri 63130
Email: holly@math.wustl.edu

DOI: 10.1090/S0002-9947-00-02691-X
PII: S 0002-9947(00)02691-X
Keywords: Isothermic, tori, Darboux transform, M\"obius geometry, moving frames, umbilic loci
Received by editor(s): August 15, 1999
Received by editor(s) in revised form: March 10, 2000
Posted: November 28, 2000
Copyright of article: Copyright 2000, American Mathematical Society

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