Some Geometry of Affine Immersion of General Co-dimension

After a careful study of some works of servaral authors on affine immersion of co-dimension one [1], co-dimension two [2], co-dimension three [3] and co-dimension four [4], we extend some of thier fundamental equations to affine immersion of genaral co-dimension p. Furthermore, we extend some theorem of Frank Dillen at el in [5] to affine immersion of general co-dimension and obtain the divisibility of the cubic forms by the second fundamental forms.