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A space-like surface in Minkowski space-time is minimal if its mean curvaturevector field is zero. Any minimal space-like surface of general type admitsspecial isothermal parameters - canonical parameters. For any minimal surfaceof general type parameterized by canonical parameters we obtain Weierstrassrepresentations - canonical Weierstrass representations via two holomorphicfunctions. We find the expressions of the Gauss curvature and the normalcurvature of the surface with respect to this pair of holomorphic functions. Wefind the relation between two pairs of holomorphic functions generating one andthe same minimal space-like surface of general type. The canonical Weierstrassformulas allow us to establish geometric correspondence between minimalspace-like surfaces of general type and classes of pairs of holomorphicfunctions in the Gauss plane.

Canonical Weierstrass representations for minimal space-like surfaces in $\RR^4_1$