A product formula for valuations on manifolds with applications to the integral geometry of the quaternionic line

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dc.creatorBernig, Andreas
dc.date2006-11-09
dc.date2008-05-23
dc.date.accessioned2026-07-07T12:58:40Z
dc.date.available2026-07-07T12:58:40Z
dc.descriptionThe 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.
dc.description18 pages, to appear in Commentarii Mathematici Helvetici
dc.identifierhttps://arxiv.org/abs/math/0611264
dc.identifierhttp://arxiv.org/abs/math/0611264
dc.identifierComm. Math. Helv. 84 (2009), 1-19
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/225319
dc.subjectDifferential Geometry
dc.subject53C65; 52A22
dc.titleA product formula for valuations on manifolds with applications to the integral geometry of the quaternionic line
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