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Sequences of harmonic maps in the 3‐sphere
Author(s) -
Dioos Bart,
Van der Veken Joeri,
Vrancken Luc
Publication year - 2015
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201400271
Subject(s) - harmonic map , mathematics , conformal map , harmonic , manifold (fluid mechanics) , surface (topology) , euclidean geometry , euclidean space , construct (python library) , sequence (biology) , space (punctuation) , pure mathematics , mathematical analysis , geometry , physics , computer science , mechanical engineering , quantum mechanics , biology , engineering , genetics , programming language , operating system
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 S 3 × S 3 . As a consequence we can construct sequences of H ‐surfaces and almost complex surfaces.