ϵ-isothermic surfaces in pseudo-Euclidean 3-space
DOI:
https://doi.org/10.17268/sel.mat.2023.01.12Keywords:
Dupin surfaces, Isothermic surfaces, lines of curvature.Abstract
In this paper, we provide a class of surfaces called ϵ-isothermic surface in the pseudo-Euclidean 3-space and we introduce the pseudo-Calapso equation. We prove that for each ϵ-isothermic surface, we can associate two solutions to the pseudo-Calapso equation. In particular, we associate solutions to the Calapso, Zoomeron and Davey-Stewartson III equations. In sequence, we classify the Dupin surfaces in pseudo-Euclidean 3-space having distinct principal curvatures and provide explicit coordinates for such surfaces.
As application of the theory, we obtain explicit solutions to the pseudo-Calapso equation and from these solutions, we provide new explicit solutions of the Zoomeron and Davey-Stewartson III equations. Moreover, we also provide explicit solutions to these equations that depend on ϵ2−holomorphic functions.
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