Spacelike constant slope surfaces were defined and completely classified inView original: http://arxiv.org/abs/1112.1504
. 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.