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Holonomy and projective symmetry in spacetimes

G S Hall and D P Lonie

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It is shown using a spacetime curvature classification and decomposition that for certain holonomy types of a spacetime, proper projective vector fields cannot exist. Existence is confirmed, by example, for the remaining holonomy types. In all except the most general holonomy type, a local uniqueness theorem for proper projective symmetry is established.


PACS

04.20.-q Classical general relativity

02.40.Dr Euclidean and projective geometries

MSC

83Cxx General relativity

51A05 General theory and projective geometries

Subjects

Mathematical physics

Gravitation and cosmology

Dates

Issue 19 (7 October 2004)

Received 10 June 2004, in final form 17 August 2004

Published 14 September 2004



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