Integral geometry in Euclidean and projective quaternionic spaces
Let \(M\) be a real compact submanifold in an \(n\)-dimensional quaternionic space \(Q^n\). The authors extend a classical result in integral geometry obtaining the volume \(M\) from its intersections with a set of \(r\)-dimensional quaternionic subspaces in \(Q^n\). Next they define the total absolute curvature of a compact quaternionic submanifold \(M\) of the projective quaternionic space \(QP^n\) and relate this curvature with the classical Lipschitz-Killing curvature.
scientific article; zbMATH DE number 1689546