Let $G_q\mathbb{R}^{n})$ be the Grassmannian of all linear $q$ dimensional subspaces of $\mathbb{R}^{n}$ and $I$ an integral invariant of $p+q-n$ dimensional submanifolds of $\mathbb{R}^{n}$. Then we give methods of evaluating Crofton type integral $ \int_{G_q(\mathbb{R}^{n})} I(M\cap L)\,{\rm d}L. $ The methods also work for various generalizations of $G_q(\mathbb{R}^{n})$ such as complex Grassmannians.
Ralph Howard
. KINEMATIC AND CROFTON FORMULAS FOR LINEAR GROUPS[J]. Acta mathematica scientia, Series B, 2025
, 45(1)
: 153
-160
.
DOI: 10.1007/s10473-025-0112-z
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