Wavefronts of traveling trajectories of geometric particles

Author:

Bi Wanying1,Wang Zhigang1ORCID

Affiliation:

1. School of Mathematical Sciences, Harbin Normal University, Harbin 150025, P. R. China

Abstract

Confining the traveling trajectory of a tachyon to the two-dimensional Lorentzian space forms, we describe the trajectory as a spacelike front in these Lorentzian space forms. Introducing the differential geometry of singular curves in Lorentzian space forms, that is, the hyperbolic space and de Sitter space, and applying the Legendrian duality theorems, we establish the moving frame along the front, whereby the definitions of the evolutes of spacelike fronts in Lorentzian space forms are presented and the geometric properties of these evolutes are investigated in detail. It is shown that these evolutes can be interpreted as wavefronts under the viewpoint of Legendrian singularity theory.

Funder

Postdoctoral Research Foundation of China

Natural Science Foundation of Heilongjiang Province

Publisher

World Scientific Pub Co Pte Lt

Subject

Physics and Astronomy (miscellaneous)

Cited by 4 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Duality and singularities of world sheets and worldlines of geometric particles along framed base curves in world hyper-sheet;International Journal of Modern Physics A;2022-06-30

2. Recognition of singularities of rectifying worldsheets generated by framed worldlines;International Journal of Modern Physics A;2021-08-19

3. Singularities and dualities of pedal curves in pseudo-hyperbolic and de Sitter space;International Journal of Geometric Methods in Modern Physics;2020-11-27

4. Generalized focal surfaces of spacelike curves lying in lightlike surfaces;Mathematical Methods in the Applied Sciences;2020-02-20

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