Frenet type formulae for $2$, $3$-planes in Minkowski space $\mathbb L^{6}$

Abstract

We prove the Frenet type formulae for smooth one-parameter family of $2$-planes or $3$-planes in the Lorentz-Minkowski space $\mathbb L^{6}$. We consider two cases separately: the planes are spacelike or the planes are timelike.