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A weighted de Rham operator leading to local potentials for Riemann and Weyl tensors
Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
Physics University of the Basque Country.
2006 (English)In: XXVIII Spanish Relativity Meeting E.R.E. A Century of Relativity Physics,2005 / [ed] Mornas, L; Alonso, JD, Melville, NY, USA: American Institute of Physics (AIP), 2006, 291- p.Conference paper (Other academic)
Abstract [en]

By defining a weighted de Rham operator for r-fold forms we obtain an associated superpotential for all tensors (considered as r-fold forms), in all dimensions. From this superpotential we deduce, in a straightforward and natural manner, the existence of 2r potentials for all r-fold forms. By specialising this result, we are able to obtain a pair of potentials for the Riemann tensor, and a single (2,3)-form potential for the Weyl tensor. This latter potential is the n-dimensional version of the double dual of the classical four dimensional (2,1)-form Lanczos potential. We also demonstrate that the new weighted de Rham operator is the natural operator to use in the Laplace-like equation for the Riemann tensor.

Place, publisher, year, edition, pages
Melville, NY, USA: American Institute of Physics (AIP), 2006. 291- p.
, AIP Conference Proceedings, ISSN 0094-243X
National Category
URN: urn:nbn:se:liu:diva-30240ISI: 000239410700021Local ID: 15745ISBN: 0-7354-0333-3OAI: diva2:251062
28th Spanish Relativity Meeting Oviedo, SPAIN SEP 06-10, 2005
Available from: 2009-10-09 Created: 2009-10-09 Last updated: 2012-08-16Bibliographically approved

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