On surfaces in the 3-dimensional Lorentz-Minkowski space

Abstract

Let Ms2 be a surface in the 3-dimensional Lorentz-Minkowski space L3 and denote by H its mean curvature vector field. This paper locally classifies those surfaces verifying the condition ΔH = λH, where λ is a real constant. The classification is done by proving that Ms2 has zero mean curvature everywhere or it is isoparametric, i.e., its shape operator has constant characteristic polynomial. © 1992 by Pacific Journal of Mathematics.