Quartic differentials and harmonic maps in conformal surface geometry

We consider codimension 2 sphere congruences in pseudo-conformal geometry that are harmonic with respect to the conformal structure of an orthogonal surface. characterise surfaces such as either $S$-Willmore surfaces, quasi-umbilical constant mean curvature 3-dimensional space forms or lightlike lightcones. then investigate Bryant's quartic differential this context and show generically is divergence free if only surface under consideration superconformal a congruence spheres. may apply previous result property.