Integral geometry under $G_2$ and $Spin(7)$
Differential Geometry
2011-08-16 v1
Abstract
A Hadwiger-type theorem for the exceptional Lie groups and is proved. The algebras of or 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.
Keywords
Cite
@article{arxiv.0803.3885,
title = {Integral geometry under $G_2$ and $Spin(7)$},
author = {Andreas Bernig},
journal= {arXiv preprint arXiv:0803.3885},
year = {2011}
}
Comments
13 pages