On the Gauss map of surfaces of revolution in the three-dimensional Minkowski space

Abstract

In this paper, we study surfaces of revolution without parabolic points in the 3-dimensional Lorentz-Minkowski space whose Gauss map N satisfies the condition Δ^IIN = AN, where Δ^II is the Laplace operator with respect to the second fundamental form and A is a real 3 × 3 matrix. More precisely we prove that such surfaces are either pseudo-Riemannian spheres S²₁ or pseudohyperbolic spaces H²₀.