A product formula for valuations on manifolds with applications to the integral geometry of the quaternionic line
Differential Geometry
2009-04-01 v2
Abstract
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.
Keywords
Cite
@article{arxiv.math/0611264,
title = {A product formula for valuations on manifolds with applications to the integral geometry of the quaternionic line},
author = {Andreas Bernig},
journal= {arXiv preprint arXiv:math/0611264},
year = {2009}
}
Comments
18 pages, to appear in Commentarii Mathematici Helvetici