Curves in Affine and Semi-Euclidean Spaces

In this paper we define centroaffine invariant arc length and curvature functions of a curve in affine n-space. Then we consider the properties and relations of the curves in affine space and Semi-Euclidean space. Using these notions and conclusions, by solving certain differential equations, we give some examples and classifications of the curves in affine 2-space and 3-space.