Following the ideas of S.-S. Chern, J. L. M. Barbosa associated a holomorphic curve in $\mathbb{C}P^m$ to a minimal immersion of a 2-sphere into a $2m$-sphere in [his 1972 paper][1]. However, his construction seems to be very unclear because of heavy use of coördinates. Are there any more coördinate-free expositions of this topic?


  [1]: http://projecteuclid.org/euclid.bams/1183534303