Translative and kinematic formulae for curvature measures of flat sections

Let X be a set of positive reach in the d-dimensional Euclidean space. We p resent formulae for the integrals of the curvature measures of flat section s of X with respect to ail translations/Euclidean motions of the sectioning flat. We consider the (generalized) curvature measures supported by the co rresponding unit normal bundle. As a special case we obtain formulae for th e spherical area measures.