The Bonnet problem for harmonic maps to the three-sphere

Autor:	Bart Dioos, Joeri Van der Veken
Rok vydání:	2019
Předmět:	Science & Technology harmonic maps 010102 general mathematics Mathematical analysis Harmonic map 01 natural sciences three-sphere 010101 applied mathematics Physical Sciences Geometry and Topology 0101 mathematics Bonnet problem MINIMAL-SURFACES Mathematics
Zdroj:	Advances in Geometry. 19:335-343
ISSN:	1615-7168 1615-715X
DOI:	10.1515/advgeom-2019-0001
Popis:	In previous work [15] the authors defined transforms for non-conformal harmonic maps from a Riemann surface into the 3-sphere. An observation from that study was that two invariants, a real and a complex function, determine a non-conformal harmonic map up to isometries of the 3-sphere. We now show that if the first invariant of a harmonic map and its transformed map are the same, then these maps are either congruent or the harmonic map belongs to a particular 1-parameter family. Inspired by this result we discuss the Bonnet problem for non-conformal harmonic maps: to what extent is a harmonic map determined by its first invariant?
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::dbe9817ca4f0da438bca9f1d18379ca0 https://doi.org/10.1515/advgeom-2019-0001 Zobrazit plný text záznamu