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Paper detail

Integral geometry under $G_2$ and $Spin(7)$

A Hadwiger-type theorem for the exceptional Lie groups $G_2$ and $Spin(7)$ is proved. The algebras of $G_2$ or $Spin(7)$ invariant, translation invariant continuous valuations are both of dimension 10. Geometrically meaningful bases are constructed and the algebra structures are computed. Finally, the kinematic formulas for these groups are determined.

preprint2008arXivOpen access
Andreas Bernig
math.DG
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Andreas Bernig

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