Dual curvature measures in hermitian integral geometry

Abstract

The local kinematic formulas on complex space forms induce the structure of a commutative algebra on the space ${\mathrm{Curv}}^{\mathrm{U}(n)\ast }$ of dual unitarily invariant curvature measures. Building on the recent results from integral geometry in complex space forms, we describe this algebra structure explicitly as a polynomial algebra. This is a short way to encode all local kinematic formulas. We then characterize the invariant valuations on complex space forms leaving the space of invariant angular curvature measures fixed.

arXiv comment15 pages; the proof of Proposition 4.4. was slightly modified