New examples of harmonic maps to the hyperbolic plane via Bäcklund transformation

2021/12/13 by Polychrou, Giannis, Papageorgiou, Effie, Fotiadis, Anestis +1 · 1 citation
#35A30 #58J70 #58J72 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2112.06601

Abstract

We study harmonic maps from a subset of the complex plane to a subset of the hyperbolic plane. In \citeFotDask, harmonic maps are related to the sinh-Gordon equation and a Bäcklund 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.

Cited by

• Explicit harmonic and wave maps into variable-curvature surfaces

Related

• Solutions of the Sinh-Gordon and Sine-Gordon equations and applications
• Geometric characterization and classification of Bäcklund transformations of sine-Gordon type
• Harmonic diffeomorphisms between pseudo-riemannian surfaces
• The Hyperbolic Geometry of the Sinh-Gordon Equation
• Harmonic maps from the product of the hyperbolic planes to the hyperbolic space