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

2013/03/28 by Svensson, Martin, Wood, John C.
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1303.7176

Abstract

We show that a harmonic map from a Riemann surface into the exceptional symmetric space G₂/\mathrm SO(4) has a J₂-holomorphic twistor lift into one of the three flag manifolds of G₂ if and only if it is `nilconformal', i.e., has nilpotent derivative. 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 G₂/\mathrm SO(4) which are not of finite uniton number, and which have lifts into any of the three twistor spaces. Harmonic maps of finite uniton number are all nilconformal; for such maps, we show that our lifts can be constructed explicitly from extended solutions.

Related

• New constructions of twistor lifts for harmonic maps
• Harmonic surfaces in the Cayley plane
• Algebraic Harmonic Maps, Totally Symmetric Harmonic Maps and a Conjecture
• Almost complex structures that are harmonic maps
• Harmonic maps of finite uniton type into inner symmetric spaces