We give a unified picture of the Frenet-Serret equations in Euclidean space and their analogues in Minkowski space that provides further insight into how and why the Minkowski versions differ from the Euclidean.
Robert J. Low. "Framing Curves in Euclidean and Minkowski Space." J. Geom. Symmetry Phys. 27 83 - 91, 2012. https://doi.org/10.7546/jgsp-27-2012-83-91