Algebraic minimal surfaces in R^4 - Small, Anthony (Mathematica Scandinavica, 2004)
There exists a natural correspondence between null curves in C^4 and "free" curves on O(1)O(1); it underlies the existence of "Weierstrass type formulae" for minimal surfaces in R^4. The construction determines correspondences for minimal surfaces in R^3, and constant mean curvature 1 surfaces in H^3; moreover it facilitates the study of symmetric minimal surfaces in R^4.