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

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

2008-03-27

arxiv.org/abs/0803.3885v1

Israel J. Math. 184 (2011), 301-316

Mathematics

Differential Geometry

13 pages

Scientific paper

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.

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