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arXiv · 1501.06526

$\mathrm{Spin}(9)$-invariant valuations on the octonionic plane

Andreas Bernig·Floriane Voide
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Abstract

The dimensions of the spaces of $k$-homogeneous $\mathrm{Spin}(9)$-invariant valuations on the octonionic plane are computed using results from the theory of differential forms on contact manifolds as well as octonionic geometry and representation theory. Moreover, a valuation on Riemannian manifolds of particular interest is constructed which yields, as a special case, an element of $\mathrm{Val}_2^{\mathrm{Spin}(9)}$.

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Andreas Bernig, Floriane Voide. 2015-01-26. $\mathrm{Spin}(9)$-invariant valuations on the octonionic plane. https://arxiv.org/abs/1501.06526

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