Canonical Weierstrass representations for minimal space-like surfaces in   $\RR^4_1$
  A space-like surface in Minkowski space-time is minimal if its mean curvature vector field is zero. Any minimal space-like surface of general type admits special isothermal parameters - canonical parameters. For any minimal surface of general type parameterized by canonical parameters we obtain Weierstrass representations - canonical Weierstrass representations via two holomorphic functions. We find the expressions of the Gauss curvature and the normal curvature of the surface with respect to this pair of holomorphic functions. We find the relation between two pairs of holomorphic functions generating one and the same minimal space-like surface of general type. The canonical Weierstrass formulas allow us to establish geometric correspondence between minimal space-like surfaces of general type and classes of pairs of holomorphic functions in the Gauss plane. 
Georgi Ganchev and Krasimir Kanchev
math.DG