# Dual curvature measures in hermitian integral geometry

## TL;DR

This paper explicitly describes the algebraic structure of dual unitarily invariant curvature measures in complex space forms, providing a compact encoding of local kinematic formulas and characterizing invariant valuations.

## Contribution

It introduces an explicit polynomial algebra structure for dual curvature measures and characterizes invariant valuations in complex space forms.

## Key findings

- Algebra structure of dual curvature measures is polynomial
- Local kinematic formulas are encoded in this algebra
- Invariant valuations are characterized within this framework

## Abstract

The local kinematic formulas on complex space forms induce the structure of a commutative algebra on the space $\mathrm{Curv}^{\mathrm{U}(n)*}$ 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.