A product formula for valuations on manifolds with applications to the integral geometry of the quaternionic line
Abstract
Description
The Alesker-Poincare pairing for smooth valuations on manifolds is expressed in terms of the Rumin differential operator acting on the cosphere-bundle. It is shown that the derivation operator, the signature operator and the Laplace operator acting on smooth valuations are formally self-adjoint with respect to this pairing. As an application, the product structure of the space of SU(2)- and translation invariant valuations on the quaternionic line is described. The principal kinematic formula on the quaternionic line is stated and proved.
18 pages, to appear in Commentarii Mathematici Helvetici
18 pages, to appear in Commentarii Mathematici Helvetici