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Sequences of harmonic maps in the 3‐sphere
Authors:Bart Dioos,Joeri Van   der   Veken,Luc Vrancken
Affiliation:1. KU Leuven, Departement Wiskunde, Leuven, Belgium;2. LAMAV, Université de Valenciennes, Campus du Mont Houy, Valenciennes Cedex 9, France
Abstract:We define two transforms of non‐conformal harmonic maps from a surface into the 3‐sphere. With these transforms one can construct, from one such harmonic map, a sequence of harmonic maps. We show that there is a correspondence between harmonic maps into the 3‐sphere, H‐surfaces in Euclidean 3‐space and almost complex surfaces in the nearly Kähler manifold urn:x-wiley:0025584X:media:mana201400271:mana201400271-math-0001. As a consequence we can construct sequences of H‐surfaces and almost complex surfaces.
Keywords:3‐sphere  almost complex surface  harmonic map  pseudo‐holomorphic curve  Primary: 58E20   Secondary: 53C42
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