Algebraic minimal surfaces in $\mathsf R^4$ - Small, Anthony (Mathematica Scandinavica, 2004)
There exists a natural correspondence between null curves in $C^4$ and "free" curves on $\mathcal O(1)\oplus \mathcal O(1)$; 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 $R^4$.