Abstract
We investigate the relationship between generalized curvatures of an arbitrary convex body K and its polar body K* in d-dimensional Euclidean space. For example, the generalized Gaus-Kronecker curvature of K is compared with the product of the generalized principal radii of curvature of K*. This leads to a generalization of the classical statement saying that the product of the equiaffine support functions of K and K* is equal to 1, provided K is sufficiently smooth and has positive Gaus-Kronecker curvature. Another consequence concerns the equality of the extended p-affine surface area of K and the q-affine surface area of K*, if pq = d2. In the special case of a smooth convex body and for p = d this result is well known in centroaffine differential geometry.
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