The Santaló-regions of a convex body

Motivated by the Blaschke-Santaló inequality, we define for a convex body K K in R n R^n and for t ∈ R t ∈ R the Santaló-regions S ( K , t ) S(K,t) of K K . We investigate the properties of these sets and relate them to a concept of affine differential geometry, the affine surface area of K K .