Caustics of translation surfaces in Euclidean \(3\)-space

Volume 10, Issue 10, pp 5300--5310 http://dx.doi.org/10.22436/jnsa.010.10.16

Publication Date: October 20, 2017 Submission Date: March 24, 2017

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Authors

Jingren Chen - School of Mathematical Sciences, Harbin Normal University, Harbin, 150025, P. R. China. Haiming Liu - School of Mathematical Sciences, Mudanjiang Normal University, Mudanjiang, 157011, P. R. China. Jiajing Miao - School of Mathematical Sciences, Mudanjiang Normal University, Mudanjiang, 157011, P. R. China.

Abstract

The aim of this paper is to classify the singularities of caustics, which have implications for a wide range of physical applications, of translation surfaces. In addition, we give a particular study on ridge point, sub-parabolic ridge point, and constant curvature line on translation surface and we find that there is no elliptic umblic on translation surface.

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Keywords

• Translation surface
• caustics
• singularity theory

MSC

•  32S25
•  53A35

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