On Lorentzian surfaces with H2=K in Minkowski 3-space

A well-known classical result classifies the surfaces in 3-space R3 with the mean curvatures H and the Gauss curvatures K satisfying H2=K as pieces of planes or two spheres. Corresponding results are given here for Lorentzian surfaces in Minkowski 3-space. This work is done by proving that all the Lorentzian surfaces with H2=K in Minkowski 3-space are null scrolls locally and can be classified into three cases, two of which have no counterparts in Euclidean space.