Mean curvatures and Gauss maps of a pair of isometric helicoidal and rotation surfaces in Minkowski 3-space

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:368

Article

Ji, Fenghui^1,2 

[1] China Univ Petr E China, Sch Math & Computat Sci, Dongying 257061, Peoples R China

[2] Kyungpook Natl Univ, Dept Math, Taegu 702701, South Korea

关键词: Minkowski space;    Helicoidal surface;    Rotation surface;    Isometry;    Mean curvature;    Gauss map;   

DOI  :  10.1016/j.jmaa.2010.03.054

来源: Elsevier

【 摘 要 】

It is proved that, in Minkowski 3-space, a CSM-helicoidal surface, i.e., a helicoidal surface under cubic screw motion is isometric to a rotation surface so that helices on the helicoidal surface correspond to parallel circles on the rotation surface. By distinguishing a CSM-helicoidal surface as three cases, that is, the case of type I, the case of type II with negative and positive pitch, the relations are discussed between the mean curvatures or Gauss maps of a pair of isometric helicoidal and rotation surface. A CSM-helicoidal surface of Case 1 or 2 and its isometric rotation surface with null axis have same mean curvatures (resp. Gauss maps) if and only if they are minimal. But each pair of isometric CSM-helicoidal surface of Case 3 and rotation surface with spacelike axis have different Gauss maps. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free