A Cauchy problem for minimal spacelike surfaces in ${\mathbb{R}}_2^4$

We give a definition of isoclinic parametric surfaces in ${\mathbb{R}}_2^4$ and prove that such an isoclinic conformal immersion comes from two holomorphic functions. A Cauchy problem was proposed and solved, namely: construct an isoclinic and minimal positive (negative) spacelike surface in ${\mathbb{R}}_2^4$, containing a given positive (negative) real analytic curve. At last, we study the important and well-known Bj"orling problem, providing some examples was given in the last section.