Surfaces of revolution in the 3-dimensional Lorentz-Minkowski space satisfying $\Delta ^{{II}} \ifmmode\expandafter\vec\else\expandafter\vecabove\fi{r} = A\ifmmode\expandafter\vec\else\expandafter\vecabove\fi{r}$

Abstract.

In this paper the surfaces of revolution without parabolic points, in the 3-dimensional Lorentz-Minkowski space are classified under the condition $\Delta ^{{II}} \ifmmode\expandafter\vec\else\expandafter\vecabove\fi{r} = A\ifmmode\expandafter\vec\else\expandafter\vecabove\fi{r}$ 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 minimal or Lorentz hyperbolic cylinders or pseudospheres of real or imaginary radius.