With commuting Killing vectors, the lapse and shift of one Killing vector are constants along the other

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dc.creatorMurchadha, Niall O
dc.date2008-10-02
dc.date2008-10-09
dc.date.accessioned2026-07-07T10:08:25Z
dc.date.available2026-07-07T10:08:25Z
dc.descriptionGiven an d-dimensional manifold with two commuting Killing vectors, together with an d - 1 dimensional submanifold in which one of the Killing vectors lies, then the lapse and shift of the second Killing vector, relative to this slice, remain constant along the orbits of the `surface' Killing vector. Alternatively, the six dot products that can be formed from the three vectors, the two Killing vectors and the normal to the submanifold, are all constants along the `surface' Killing vector.
dc.descriptionThe key result in this paper was previously discovered by Beig and Chrusciel using a different approach. I add the appropriate reference and a short discussion of their derivation
dc.identifierhttps://arxiv.org/abs/0810.0505
dc.identifierhttp://arxiv.org/abs/0810.0505
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/170986
dc.subjectGeneral Relativity and Quantum Cosmology
dc.subjectDifferential Geometry
dc.titleWith commuting Killing vectors, the lapse and shift of one Killing vector are constants along the other
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