Relation between the minimal Lorentz surfaces in ${\mathbb{R}}_2^4$ and ${\mathbb{R}}_1^3$

Abstract

In this paper we give Weierstrass-type representation formulas for the null curves and for the minimal Lorentz surfaces in the Minkowski 3-space ${\mathbb{R}}_1^3$ using real-valued functions. Applying the Weierstrass-type representations for the null curves, we find a correspondence between the null curves in ${\mathbb{R}}_2^4$ and the pairs of null curves in ${\mathbb{R}}_1^3$. Based on this correspondence, we obtain a relation between the minimal Lorentz surfaces in ${\mathbb{R}}_2^4$ and the pairs of minimal Lorentz surfaces in ${\mathbb{R}}_1^3$.

15 pages