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arXiv · 2112.06601

New examples of harmonic maps to the hyperbolic plane via B\"acklund transformation

Giannis Polychrou·Effie Papageorgiou·Anestis Fotiadis·Costas Daskaloyannis
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Abstract

We study harmonic maps from a subset of the complex plane to a subset of the hyperbolic plane. In \cite{FotDask}, harmonic maps are related to the sinh-Gordon equation and a B{\"a}cklund transformation is introduced, which connects solutions of the sinh-Gordon and sine-Gordon equation. We develop this machinery in order to construct new harmonic maps to the hyperbolic plane.

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Giannis Polychrou, Effie Papageorgiou, Anestis Fotiadis, Costas Daskaloyannis. 2021-12-13. New examples of harmonic maps to the hyperbolic plane via B\"acklund transformation. https://arxiv.org/abs/2112.06601

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