New examples of harmonic maps to the hyperbolic plane via B\"acklund transformation
Differential Geometry
2023-06-02 v3
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.
Keywords
Cite
@article{arxiv.2112.06601,
title = {New examples of harmonic maps to the hyperbolic plane via B\"acklund transformation},
author = {Giannis Polychrou and Effie Papageorgiou and Anestis Fotiadis and Costas Daskaloyannis},
journal= {arXiv preprint arXiv:2112.06601},
year = {2023}
}