We determine surfaces of genus zero in four-dimensional hyperkähler manifolds whose twistor lifts are harmonic sections. As corollary, we prove that a surface of genus zero in four-dimensional Euclidean space is twistor holomorphic if its twistor lift is harmonic section.
"On Surfaces of Low Genus Whose Twistor Lifts are Harmonic Sections." J. Geom. Symmetry Phys. 17 35 - 43, 2010. https://doi.org/10.7546/jgsp-17-2010-35-43