The Gauss map and spacelike surfaces with prescribed mean curvature in Minkowski $3$-space

Abstract

For an oriented spacelike surface in Minkowski 3-space L 3 , the Gauss map G is defined to be a mapping of M into the unit pseudosphere H in L 3 , which assigns to each point p of M the point in H obtained by translating the timelike unit normal vector at p to the origin. Our primary object of this paper is to prove a representation formula for spacelike surfaces with prescribed mean curvature in terms of their Gauss maps