On Lorentz GCR surfaces in Minkowski 3-space
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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.
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.
참고문헌 (19)
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