Singularity properties of Lorentzian Darboux surfaces in Lorentz–Minkowski spacetime

被引：0
|
作者：
Yanlin Li
Xuelian Jiang
Zhigang Wang
机构：
[1] Hangzhou Normal University,School of Mathematics
[2] Harbin Normal University,School of Mathematical Sciences
来源：
Research in the Mathematical Sciences | 2024年 / 11卷
关键词：
Darboux frame; Lorentzian Darboux surfaces; Legendrian duality; Swallowtail; 53A35; 58C25;
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学科分类号：
摘要：
In this paper, by virtue of unfolding theory in singularity theory, we investigate the singularities of five special surfaces generated by a regular curve lying on a spacelike hypersurface in Lorentz–Minkowski 4-space. Using two kinds of extended Lorentzian Darboux frames along the curve as tools, five new invariants are obtained to characterize the singularities of five special surfaces and their geometric meanings are discussed in detail. In addition, some dual relationships between a normal curve of the original curve and five surfaces are revealed under the meanings of Legendrian duality.
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