# Affine torsion

One of the differential invariants of a curve in equi-affine space:

$$\tau = - ( \mathbf r ^ {\prime\prime} , \mathbf r ^ {\prime\prime\prime} ,\ \mathbf r ^ {\prime\prime\prime\prime} ) ,$$

where the primes denote differentiation with respect to the affine parameter of the position vector of the curve. Similar concepts are introduced for curves in spaces with other fundamental groups such as centro-affine.