Define an k-Torsion as a measure of how much a parametrically defined curve $x(t)$ where $t$ is a real scalar and $x$ is a vector in $R^n$ deviates from the locally encapsulating k-dimensional hyperplane at t.
How do you measure k-torsion in n dimensional parametric curves? It's trivial to measure it $R^3$ but the use of the cross product doesn't generalize easily (wedge products require a lot of vectors).