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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.
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참고문헌 (19)
참고문헌 신청
K. N. Boyadzhiev / 2007 / Equiangular surfaces, self-similar surfaces, and the geometry of seashells / Coll. Math. J 38(4):265~271
B. Y. Chen / 1973 / Geometry of Submanifolds / Marcel Dekker
B. Y. Chen / 2001 / Constant-ratio hypersurfaces / Soochow J. Math 27(4):353~362
F. Dillen / 2009 / Surfaces in S2 × R with a canonical principal dirention / Ann. Global Anal. Geom 35(4):381~396
F. Dillen / 2007 / Constant angle surfaces in S2 × R / Monatsh. Math 152(2):89~96
B. Y. Chen / 1973 / Geometry of Submanifolds / Marcel Dekker
B. Y. Chen / 2001 / Constant-ratio hypersurfaces / Soochow J. Math 27(4):353~362
F. Dillen / 2009 / Surfaces in S2 × R with a canonical principal dirention / Ann. Global Anal. Geom 35(4):381~396
F. Dillen / 2007 / Constant angle surfaces in S2 × R / Monatsh. Math 152(2):89~96
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