New Isothermic surfaces in S3


  • Armando M. V. Corro IME, Universidade Federal de Goiás, Caixa Postal 131, 74001-970, Goiania, GO, Brazil.
  • Marcelo Lopes Ferro IME, Universidade Federal de Goiás, Caixa Postal 131, 74001-970, Goiania, GO, Brazil.



Isothermic surfaces , Ribaucour transformations, Dupin surfaces, Calapso equation


In this paper, we consider a method of constructing isothermic surfaces in S3 based on Ribaucour transformations.

By applying the theory to the flat torus, we obtain two family of complete isothermic surfaces in

S3. One four-parameter family of complete isothermic surfaces that contains n-bubble surfaces inside and outside of the torus. We also get another four-parameter of complete isothermic surfaces which are Dupin surfaces. As aplication we obtain explicit solutions of the Calapso equation.


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How to Cite

V. Corro, A. M., & Lopes Ferro, M. (2023). New Isothermic surfaces in S3. Selecciones Matemáticas, 10(01), 114 - 128.