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

Authors
Bernstein, H
Citation
H. Bernstein, Non-special, non-canal isothermic tori with spherical lines of curvature, T AM MATH S, 353(6), 2001, pp. 2245-2274
Citations number
22
Categorie Soggetti
Mathematics
Journal title
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
ISSN journal
00029947 → ACNP
Volume
353
Issue
6
Year of publication
2001
Pages
2245 - 2274
Database
ISI
SICI code
0002-9947(2001)353:6<2245:NNITWS>2.0.ZU;2-N
Abstract
This article examines isothermic surfaces smoothly immersed in Mobius space . It finds explicit examples of non-special, non-canal isothermic tori with spherical lines of curvature in two systems by analyzing Darboux transform s of Dupin tori. In addition, it characterizes the property of spherical li nes of curvature in terms of differential equations on the Calapso potentia l of the isothermic immersion, and investigates the effect of classical tra nsformations on this property.