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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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


Author: Holly Bernstein
Journal: Trans. Amer. Math. Soc. 353 (2001), 2245-2274
MSC (1991): Primary 53A05; Secondary 51B10, 58G37
Published electronically: November 28, 2000
MathSciNet review: 1814069
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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: http://dx.doi.org/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
Published electronically: November 28, 2000
Article copyright: © Copyright 2000 American Mathematical Society