Fundamental theorem of spacelike curves in Lorentz-Minkowski space

Atsufumi Honda

Published 2019-05-08Version 1

In Lorentz-Minkowski 3-space, the fundamental theorem of spacelike curves is known, if they have spacelike, timelike or lightlike curvature vector fields. However, such a theory cannot be applied to spacelike curves with type-changing curvature vector field. To fill the gap, in this paper, we introduce the pseudo-torsion functions along spacelike curves whose curvature vector field has isolated lightlike points, and prove the fundamental theorem for them. As an application, we obtain a necessary and sufficient condition for real analytic spacelike curves to be planar.