Kinematic formulas on the quaternionic plane
Andreas Bernig, Gil Solanes
TL;DR
This paper develops new bases for invariant valuations on the quaternionic plane and derives comprehensive kinematic formulas, advancing the understanding of geometric measures in quaternionic spaces.
Contribution
It introduces various bases for invariant valuations and provides a complete set of kinematic formulas specific to the quaternionic plane.
Findings
New bases for invariant valuations are constructed.
A complete set of kinematic formulas is derived.
The results enhance geometric measure theory in quaternionic spaces.
Abstract
We introduce different bases for the vector space of -invariant, translation invariant continuous valuations on the quaternionic plane and determine a complete set of kinematic formulas.
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