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تسجيل مستخدم جديد$mathrm{Spin}(9)$-invariant valuations on the octonionic plane
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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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