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

• Autores: Andreas Bernig
• Localización: Commentarii mathematici helvetici, ISSN 0010-2571, Vol. 84, Nº 1, 2009, págs. 1-19
• Idioma: inglés
• DOI: 10.4171/cmh/150
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• Resumen

  • The Alesker�Poincaré 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 H is stated and proved.