Algebraic minimal surfaces in R4

Abstract

There exists a natural correspondence between null curves in C4 and "free" curves on O(1)⊕O(1); it underlies the existence of "Weierstrass type formulae" for minimal surfaces in R4. The construction determines correspondences for minimal surfaces in R3, and constant mean curvature 1 surfaces in H3; moreover it facilitates the study of symmetric minimal surfaces in R4