Ribaucour surfaces of harmonic type
| Autor: | Armando M. V. Corro, Carlos M. C. Riveros, Karoline V. Fernandes |
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| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | International Journal of Mathematics. 33 |
| ISSN: | 1793-6519 0129-167X |
| DOI: | 10.1142/s0129167x22500069 |
| Popis: | We introduce the class of Ribaucour surfaces of harmonic type (in short HR-surfaces) that generalizes the Ribaucour surfaces related to a problem posed by Élie Cartan. We obtain a Weierstrass-type representation for these surfaces which depends on three holomorphic functions. As application, we classify the HR-surfaces of rotation, present examples of complete HR-surfaces of rotation with at most two isolated singularities and an example of a complete HR-surface of rotation with one catenoid type end and one planar end. Also, we present a 5-parameter family of cyclic HR-surfaces foliated by circles in non-parallel planes. Moreover, we classify the isothermic HR-surfaces with planar lines of curvature. |
| Databáze: | OpenAIRE |
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