1. Dual Curvature Measures in Hermitian Integral Geometry
- Author
-
Joseph H. G. Fu, Andreas Bernig, and Gil Solanes
- Subjects
Algebraic structure ,010102 general mathematics ,Mathematical analysis ,Kinematics ,Curvature ,01 natural sciences ,Hermitian matrix ,Integral geometry ,Complex space ,0103 physical sciences ,010307 mathematical physics ,0101 mathematics ,Commutative algebra ,Invariant (mathematics) ,Mathematics - Abstract
The local kinematic formulas on complex space forms induce the structure of a commutative algebra on the space CurvU(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.
- Published
- 2017