Caustics of de Sitter spacelike curves in Minkowski 3-space


Authors

Jiajing Miao - School of Mathematics, Mudanjiang Normal University, 157011 Mudanjiang, P. R. China. Haiming Liu - School of Mathematics, Mudanjiang Normal University, 157011 Mudanjiang, P. R. China.


Abstract

In this paper, we consider evolutes of spacelike curves in de Sitter 2-space. Applying the theory of singularity theory, we find that these evolutes can be seen as one dimensional caustics which are locally diffeomorphic to lines or ordinary cusps. We establish the relationships between singularities of caustics and geometric invariants of curves under the action of the Lorentz group.


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ISRP Style

Jiajing Miao, Haiming Liu, Caustics of de Sitter spacelike curves in Minkowski 3-space, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 6, 4286--4294

AMA Style

Miao Jiajing, Liu Haiming, Caustics of de Sitter spacelike curves in Minkowski 3-space. J. Nonlinear Sci. Appl. (2016); 9(6):4286--4294

Chicago/Turabian Style

Miao, Jiajing, Liu, Haiming. "Caustics of de Sitter spacelike curves in Minkowski 3-space." Journal of Nonlinear Sciences and Applications, 9, no. 6 (2016): 4286--4294


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