Integral geometry of exceptional spheres

Gil Solanes, Thomas Wannerer

Research output: Contribution to journalArticleResearchpeer-review

5 Citations (Scopus)


The algebras of valuations on S6and S7invariant under the actions of G2and Spin(7) are shown to be isomorphic to the algebra of translation-invariant valuations on the tangent space at a point invariant under the action of the isotropy group. This is in analogy with the cases of real and complex space forms, suggesting the possibility that the same phenomenon holds in all Riemannian isotropic spaces. Based on the description of the algebras the full array of kinematic formulas for invariant valuations and curvature measures in S6and S7is computed. A key technical point is an extension of the classical theorems of Klain and Schneider on simple valuations.

Original languageEnglish
Pages (from-to)137-191
Number of pages55
JournalJournal of Differential Geometry
Issue number1
Publication statusPublished - 2021


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