Tensorial Curvature Measures in Integral Geometry

The tensorial curvature measures are tensor-valued generalizations of the curvature measures of convex bodies. On convex polytopes, there exist further generalizations some of which also have continuous extensions to arbitrary convex bodies. We prove complete sets of kinematic and Crofton formulae for the (generalized) tensorial curvature measures. By globalization of these integral geometric formulae, we derive complete sets of the corresponding formulae for the total tensorial curvature measures, the well-known Minkowski tensors.