A Weierstrass representation theorem for Lorentz surfaces

Abstract

We consider functions with values in the algebra of Lorentz numbers which are differentiable with respect to the algebraic structure of as an analogue of holomorphic functions. Then we apply these functions to prove a Weierstrass representation theorem for Lorentz surfaces immersed in the space . In the proof we essentially follow the model of the complex numbers. We apply our representation theorem to construct explicit minimal immersions.