On the Derivative Formulas of the Rotation Minimizing Frame in Lorentz-Minkowski 3-Space

Abstract

The main intention of this paper is to analyze integrability for the derivative formulas of the rotation minimizing frame in the Lorentz-Minkowski 3-space. As far as we know, no one has yet given a method to study their integrability in the Lorentz-Minkowski 3-space. So, we introduce the coordinate system in order to provide a tool for studying the integrability. As an application, the position vectors of some special curves having an important place in mathematical and physical research are obtained in the natural representation form. Finally, we support our work with examples.