Relation between the minimal Lorentz surfaces in R⁴₂ and R³₁

In this paper we give Weierstrass-type representation formulas for the null curves and for the minimal Lorentz surfaces in the Minkowski 3-space R³₁ using real-valued functions. Applying the Weierstrass-type representations for the null curves, we find a correspondence between the null curves in R⁴₂ and the pairs of null curves in R³₁. Based on this correspondence, we obtain a relation between the minimal Lorentz surfaces in R⁴₂ and the pairs of minimal Lorentz surfaces in R³₁.