Kinematische Berührung im Äquiaffinen. (Kinematical contact in the equiaffine) (Q910029)

In previous papers the author has considered some contact kinematic formulae in spaces of constant curvature [Abh. Math. Semin. Univ. Hamb. 58, 255-266 (1988; Zbl 0644.53064); ibid. 59, 107-122 (1989)] where more references are given]. In the present paper he considers analogous questions in affine space under the group of volume-preserving affinities. In the case of two curves in the real affine plane, the contact measure is given in terms of affine lengths and affine curvatures of the given curves. The case of parabolas which hyperosculate a given curve in the affine plane is also considered. In a similar way, parallel supporting planes of closed convex surfaces in affine n-dimensional space are treated.