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arXiv:1404.1357 [math.DG]AbstractReferencesReviewsResources

Affine transformations and parallel lightlike vector fields on compact Lorentzian $3$-manifolds

Charles Boubel, Pierre Mounoud

Published 2014-04-04, updated 2015-06-25Version 3

We describe the compact Lorentzian $3$-manifolds admitting a parallel lightlike vector field. The classification of compact Lorentzian $3$-manifolds admitting non-isometric affine diffeomorphisms follows, together with the complete description of these morphisms. Such a Lorentzian manifold is in some sense an equivariant deformation of a flat one.

Comments: 37p
Journal: Transactions of the American Mathematical Society, American Mathematical Society, 2016, pp.1
Categories: math.DG
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