On spacelike constant slope surfaces and Bertrand curves in Minkowski 3-space

Details On spacelike constant slope surfaces and Bertrand curves in Minkowski 3-space On spacelike constant slope surfaces and Bertrand curves in Minkowski 3-space

2011-12-07

arxiv.org/abs/1112.1504v2

Mathematics

Differential Geometry

22 pages, 4 figures

Scientific paper

Spacelike constant slope surfaces were defined and completely classified in [8]. In this work, firstly we show that timelike Bertrand curves and spacelike Bertrand curves can be constructed from unit speed spacelike curves on the unit pseudo-Riemannian hyperbolical space H2 and from unit speed spacelike and timelike curves on the unit pseudo-Riemann sphere S21, respectively. Secondly, we investigate the relations between Bertrand curves and spacelike constant slope surfaces in E31. Moreover we illustrate some examples of our main results and the corresponding pictures are drawn by using Mathematica.

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