Contact measures in isotropic spaces

© 2017 Elsevier Inc. We revisit the contact measures introduced by Firey, and further developed by Schneider and Teufel, from the perspective of the theory of valuations on manifolds. This reveals a link between the kinematic formulas for area measures studied by Wannerer and the integral geometry of curved isotropic spaces. As an application we find explicitly the kinematic formula for the surface area measure in Hermitian space.