Harmonic maps into the exceptional symmetric space G2/SO(4)

Martin Svensson, John C. Wood

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

Abstrakt

We show that a harmonic map from a Riemann surface into the exceptional symmetric space $G_2/{\mathrm SO}(4)$ has a $J_2$-holomorphic twistor lift into one of the three flag manifolds of $G_2$ if and only if it is `nilconformal', i.e., has nilpotent derivative. The class of nilconformal maps includes those of finite uniton number studied by N. Correia and R. Pacheco, however we exhibit examples which are not of finite uniton number. Then we find relationships with almost complex maps from a surface into the 6-sphere; this enables us to construct examples of nilconformal harmonic maps into $G_2/{\mathrm SO}(4)$ which are not of finite uniton number, and which have lifts into any of the three twistor spaces.
Originalsprog Engelsk Journal of the London Mathematical Society 91 1 291-319 0024-6107 https://doi.org/10.1112/jlms/jdu073 Udgivet - 2015

Bibliografisk note

(Submitted on 28 Mar 2013 (v1), last revised 6 Sep 2013 (this version, v2))

Fingeraftryk

Dyk ned i forskningsemnerne om 'Harmonic maps into the exceptional symmetric space G2/SO(4)'. Sammen danner de et unikt fingeraftryk.