We study the twistor map of Penrose, T: CP 3 -> S 4 and show that the complex 2-plane field in CP 3 orthogonal to the fibers of T is a holomorphic nonintegrable 2-plane field. We then show that every horizontal holomorphic curve in CP 3 projects under T to be a minimal surface in S 4 . Finally, we use the Riemann-Roch theorem to construct, for any compact Riemann surface A/ 2 , a holomorphic horizontal curve :
No takes yet. Share an insight, caveat, or question.
Robert L. Bryant (1982) studied this question.