The Riemann-Lanczos Problem as an Exterior Differential System with Examples in 4 and 5 Dimensions

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dc.creatorDolan, P
dc.creatorGerber, A
dc.date2002-12-12
dc.date.accessioned2026-07-07T03:27:25Z
dc.date.available2026-07-07T03:27:25Z
dc.descriptionThe key problem of the theory of exterior differential systems (EDS) is to decide whether or not a system is in involution. The special case of EDSs generated by one-forms (Pfaffian systems) can be adequately illustrated by a 2-dimensional example. In 4 dimensions two such problems arise in a natural way, namely, the Riemann-Lanczos and the Weyl-Lanczos problems. It is known from the work of Bampi and Caviglia that the Weyl-Lanczos problem is always in involution in both 4 and 5 dimensions but that the Riemann-Lanczos problem fails to be in involution even for 4 dimensions. However, singular solutions of it can be found. We give examples of singular solutions for the Goedel, Kasner and Debever-Hubaut spacetimes. It is even possible that the singular solution can inherit the spacetime symmetries as in the Debever-Hubaut case. We comment on the Riemann-Lanczos problem in 5 dimensions which is neither in involution nor does it admit a 5-dimensional involution of Vessiot vector fields in the generic case.
dc.description26 pages, latex, no figures
dc.identifierhttps://arxiv.org/abs/gr-qc/0212054
dc.identifierhttp://arxiv.org/abs/gr-qc/0212054
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/34422
dc.subjectGeneral Relativity and Quantum Cosmology
dc.titleThe Riemann-Lanczos Problem as an Exterior Differential System with Examples in 4 and 5 Dimensions
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