An Integral Characterization for the Curves on the Hyperbolic Sphere 30H in the Minkowski Space-time 41E

Copyright © 2014 Mustafa Kazaz et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In this paper, we showed that a hyperbolic spherical curve in the Minkowski space-time 41E can be given by Frenet-like equations of a space-like curve in the Minkowski 3-space 31E. Thus, finding an integral characterization for a hyperbolic spherical 41E- curve is identical to finding it for a space-like 3 1E-curve. For a unit speed space-like curve (s)α in 31E with ' ()s =Tα, we showed that (s)α is a space-like Frenet curve with curvature ()sκ and torsion ()sτ if and only if there are constant vectors a and b such tha