We solve the Bjorling problem for timelike surfaces in the Lorentz-Minkowski space through a split-complex representation formula obtained for this kind of surface. Our approach uses the split-complex numbers and natural split-holomorphic extensions. As applications, we show that the minimal timelike surfaces of revolution as well as minimal ruled timelike surfaces can be characterized as solutions of certain adequate Bjorling problems in the Lorentz-Minkowski space.
R. M. B. Chaves, M. P. Dussan and M. Magid, The Bjorling problem for timelike surfaces in the Lorentz-Minkowski space, J. Math. Anal. Appl. 377 (2011), no. 2, 481–494.