Pairs of sets of constant relative width (Q1820436)

Let S be a centrally symmetric convex body in Euclidean d-space \(E^ d\). Then the author defines a pair of closed convex sets (X,Y) to be a pair of constant width relative to S, if for their support function h holds: \(h(X,u)+h(Y,-u)=\lambda h(S,u)\) for some \(\lambda >0\) and all directions u. The author shows that there are interesting connections between pairs of constant width relative to S and the summands A, B of the Minkowski sum \(A+B=S\).