On space-like generalized constant ratio hypersufaces in Minkowski spaces

A hypersurface in a Euclidean space $\mathbb{E}^{n+1}$ is said to be a generalized constant ratio (GCR) hypersurface if the tangential part of its position vector is one of its principle directions. In this work, we move the study of generalized constant ratio hypersurfaces started in \cite% {YuFu2014GCRS} into the Minkowski space. First, we get some geometrical properties of non-degenerated GCR hypersurfaces in an arbitrary dimensional Minkowski space. Then, we obtain complete classification of GCR surfaces in the Minkowski 3-space. We also give some explicit examples.