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Integral geometry under G2 and Spin(7)

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Abstract

A Hadwiger-type theorem for the exceptional Lie groups G2 and Spin(7) is proved. The algebras of G2 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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Authors and Affiliations

  1. Institut für Mathematik, Johann Wolfgang Goethe-Universität, Frankfurt Robert-Mayer-Str. 10, 60054, Frankfurt, Germany

    Andreas Bernig

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  1. Andreas Bernig
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Correspondence to Andreas Bernig.

Additional information

Supported by the Schweizerischer Nationalfonds grants PP002-114715/1 and 200020-121506.

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Bernig, A. Integral geometry under G2 and Spin(7). Isr. J. Math. 184, 301–316 (2011). https://doi.org/10.1007/s11856-011-0069-6

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  • DOI: https://doi.org/10.1007/s11856-011-0069-6

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