Affine geometry of curves

In the mathematical field of differential geometry, the affine geometry of curves is the study of curves in an affine space, and specifically the properties of such curves which are invariant under the special affine group ${\displaystyle {\mbox{SL}}(n,\mathbb {R} )\ltimes \mathbb {R} ^{n}.}$

In the classical Euclidean geometry of curves, the fundamental tool is the Frenet–Serret frame. In affine geometry, the Frenet–Serret frame is no longer well-defined, but it is possible to define another canonical moving frame along a curve which plays a similar decisive role. The theory was developed in the early 20th century, largely from the efforts of Wilhelm Blaschke and Jean Favard.