The Santalo-regions of a convex body

Motivated by the Blaschke-Santal'o inequality, we define for a convex body K in ${\mathbf{R}}^n$ and for $t\in \mathbf{R}$ the Santal'o-regions S(K,t) of K. We investigate properties of these sets and relate them to a concept of Affine Differential Geometry, the affine surface area of K.