General Affine Differential Geometry for Low Codimension Immersions.
We present a fundamental theory of curves in the affine plane and the affine space, equipped with the general-affine groups and , respectively. We define general-affine length parameter and curvatures and show how such invariants determine the curve up to general-affine motions. We then study the extremal problem of the general-affine length functional and derive a variational formula. We give several examples of curves and also discuss some relations with equiaffine treatment and projective...