ON LORENTZ GCR SURFACES IN MINKOWSKI 3-SPACE
ON LORENTZ GCR SURFACES IN MINKOWSKI 3-SPACE
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DOI：
10.4134/bkms.2016.53.1.227
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发表时间：
2016-01
影响因子：
0.5
通讯作者：
Yu Fu;Dan Yang
中科院分区：
文献类型：
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作者：
Yu Fu;Dan Yang
抽象的。广义常比曲面(Gcr曲面)是由位置向量的切线分量在曲面上每个点的切线方向都是原点这一性质所要求的，详见[8]。本文通过求解一些微分方程组，给出了三维ff空间中Lorentz GCR曲面的一个完备的类fi正离子。此外，证明了洛伦兹GCR曲面上的fl是柱面的开口部分，而CMC Lorentz GCR曲面是旋转曲面。1.引言恒斜率曲面的概念是由Munteanu在[15]中提出的，它是指其法线与位置向量成恒定角的曲面。特别是，Munteanu很好地刻画了欧几里得3-空间中的常值斜面。在Munteanu工作的启发下，作者在[10，11]中对Minkowski 3-空间R31中的常斜面进行了分类.另一方面，陈碧云在[3]中引入了常比子流形的概念，这是由其位置向量的切线分量和法向分量的长度之比为常量的性质而得到的(fifiNed).陈[3]还得到了R中常比超曲面的类fi正
Abstract. A generalized constant ratio surface (GCR surface) is definedby the property that the tangential component of the position vector is aprincipal direction at each point on the surface, see [8] for details. In thispaper, by solving some differential equations, a complete classificationof Lorentz GCR surfaces in the three-dimensional Minkowski space ispresented. Moreover, it turns out that a flat Lorentz GCR surface is anopen part of a cylinder, apart from a plane and a CMC Lorentz GCRsurface is a surface of revolution. 1. IntroductionThe concept of constant slope surfaces is introduced by Munteanu in [15],which are the surfaces whose normal makes a constant angle with the positionvector. In particular, Munteanu gave a nice characterization of constant slopesurfaces in Euclidean 3-space. Motivated by Munteanu’s work, constant slopesurfaces in Minkowski 3-space R 31 were classified by the authors in [10, 11].On the other hand, B. Y. Chen introduced in [3] the concept of constant ratiosubmanifolds, which is defined by the property that the ratio of the length ofthe tangential and normal components of its position vector is constant. Chen[3] also obtained the classification of constant ratio hypersurfaces in R