Isothermic Surfaces Associated with the Cylinder Obtained by Ribaucour Transformations

In this paper we consider a method for obtaining isothermic surfaces based on the Ribaucour transformations. By applying the theory to the cylinder, we obtain two families of complete isothermic surfaces. In the first family we have bubbletons surfaces and surfaces with planar ends. In second family...

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Bibliographic Details
Published inMathematical Notes Vol. 114; no. 5-6; pp. 728 - 747
Main Authors Corro, A. M. V., Ferro, M. L.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.12.2023
Springer Nature B.V
Subjects
14/34
639/766/189
639/766/530
639/766/747
Cylinders
Mathematics
Mathematics and Statistics
isothermic surface
Ribaucour transformation
Dupin surface
Calapso equation
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Summary:In this paper we consider a method for obtaining isothermic surfaces based on the Ribaucour transformations. By applying the theory to the cylinder, we obtain two families of complete isothermic surfaces. In the first family we have bubbletons surfaces and surfaces with planar ends. In second family, we get Dupin surfaces. As an application, we provide new explicit solutions to the Calapso equation.
ISSN:0001-4346
1067-9073
1573-8876
DOI:10.1134/S0001434623110093