Sequences of harmonic maps in the 3‐sphere | Zendy

Dioos Bart | Zendy; Van der Veken Joeri | Zendy; Vrancken Luc | Zendy

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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 , conformal map , harmonic , manifold (fluid mechanics) , surface (topology) , euclidean space , mathematics , euclidean geometry , construct (python library) , sequence (biology) , space (punctuation) , mathematical analysis , pure mathematics , topology (electrical circuits) , geometry , physics , combinatorics , computer science , quantum mechanics , engineering , mechanical engineering , biology , 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.

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