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.
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Acknowledgements
Andreas Bernig was supported by DFG grant BE 2484/5-2. Joseph H.G. Fu was supported by NSF grant DMS-1406252. Gil Solanes is a Serra Húnter Fellow and was supported by FEDER-MINECO grant MTM2015-66165-P.
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Bernig, A., Fu, J.H.G., Solanes, G. (2018). Dual Curvature Measures in Hermitian Integral Geometry. In: Bianchi, G., Colesanti, A., Gronchi, P. (eds) Analytic Aspects of Convexity. Springer INdAM Series, vol 25. Springer, Cham. https://doi.org/10.1007/978-3-319-71834-7_1
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DOI: https://doi.org/10.1007/978-3-319-71834-7_1
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