A fourth order family of minimal surfaces in the 3-sphere

Abstract

This is a preliminary note on a family of minimal surfaces in the 3-sphere defined by a compatible fourth order equation. The minimal surfaces are geometrically characterized either by having a surface of revolution like induced metric, or by having a flat structure 3-web. We observe that the structure equation un-couples for a natural choice of frame. The analysis is reduced to the associated curves in the 2-sphere defined by a rational third order ODE on the curvature.

arXiv commentThis note is incorporated into arXiv:1309.6606