Harmonic maps into G2/SO(4) and their twistor lifts

Martin Svensson, University of Southern Denmark. Part of the geometry seminar series.

Burstall and Rawnsley have shown how the canonically fibered flag manifolds sit inside the twistor space of a compact, simply connected inner Riemannian symmetric space. It is known that a harmonic map from a surface into an inner Riemannian symmetric space of classical type has a twistor lift into such a flag manifold if and only if it is nilconformal in the sense that its derivative is nilpotent. In this talk, I will show that this result can be generalised to harmonic maps into the exceptional inner symmetric space $G_2/SO(4)$. I will describe the structure of the canonically fibered flag manifolds over this space and the construction of the twistor lifts of nilconformal harmonic maps. I will also show how almost complex maps into $S^6$ can be used to construct harmonic maps into $G_2/SO(4)$. The talk will be based on joint work with John C. Wood.

Martin Svensson, University of Southern Denmark