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Three-dimensional Lorentz manifolds admitting a parallel null vector field

M Chaichi1, E García-Río2 and M E Vázquez-Abal2

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Curvature properties of three-dimensional Lorentz manifolds admitting a parallel degenerate line field are examined. A complete characterization of those manifolds being locally symmetric or locally conformally flat is obtained. The results of this study show nice families of examples of such properties within the Lorentzian setting.


PACS

02.40.Ky Riemannian geometries

02.40.Sf Manifolds and cell complexes

02.10.Ud Linear algebra

MSC

53C21 Methods of Riemannian geometry, including PDE methods; curvature restrictions (See also 58J60)

53C50 Lorentz manifolds, manifolds with indefinite metrics

Subjects

Mathematical physics

Dates

Issue 4 (28 January 2005)

Received 23 July 2004, in final form 25 November 2004

Published 12 January 2005



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