On Lorentz GCR surfaces in Minkowski 3-space
Bull. Korean Math. Soc. 2016 Vol. 53, No. 1, 227-245
https://doi.org/10.4134/BKMS.2016.53.1.227
Printed January 31, 2016
Yu Fu and Dan Yang
Dongbei University of Finance and Economics, Shenyang University
Abstract : 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
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