Möbius inversion of surfaces in the Minkowski 3-space

We define and present some proprieties of the Möbius inversion of surfaces in the Minkowski 3-space. We prove that the Möbius inversion preserves the lines of principal curvature and the locus of points where the metric is degenerate, but it does not preserve the parabolic set. For ovaloids, we show that it is possible to translate the surface so that the inversion remains an ovaloid.