Bulletin of the
Korean Mathematical Society BKMS

A generalized constant ratio surface (GCR surface) is defined by the property that the tangential component of the position vector is a principal direction at each point on the surface, see \cite{FM11} for details. In this paper, by solving some differential equations, a complete classification of Lorentz GCR surfaces in the three-dimensional Minkowski space is presented. Moreover, it turns out that a flat Lorentz GCR surface is an open part of a cylinder, apart from a plane and a CMC Lorentz GCR surface is a surface of revolution.

Keywords: surfaces of revolution, GCR surfaces, Lorentz surfaces, constant slope surfaces, constant angle surfaces

MSC numbers: 53B30, 53C40, 53C42