Curves and surfaces of spacelike curves according to Bishop frame and their singularities

Volume 10, Issue 9, pp 5020--5037 http://dx.doi.org/10.22436/jnsa.010.09.39

Publication Date: September 25, 2017 Submission Date: November 28, 2016

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Authors

Haiming Liu - School of Mathematics, Mudanjiang Normal University, 157011 Mudanjiang, P. R. China. Jiajing Miao - School of Mathematics, Mudanjiang Normal University, 157011 Mudanjiang, P. R. China. Donghe Pei - School of Mathematics and Statistics, Northeast Normal University, 130024 Changchun, P. R. China.

Abstract

Legendrian dualities between pseudo-spherical images of spacelike curves in Minkowski \(3\)-space are investigated by using the theory of Legendrian duality. Moreover, the singularities of parallel lightcone developables, dual surface, Bishop pseudo-spherical Darboux images and Bishop pseudo-spherical images, which are generated by spacelike curves, are classified from the viewpoints of wave fronts and caustics, and we also give some more detail descriptions on the conditions of those singularities. Finally, some properties of parallel slant helix are given.

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Keywords

• Spacelike curves
• Minkowski \(3\)-space
• Bishop frame
• Legendrian dualities

MSC

•  32S25
•  53A35

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