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On Geometry of Flat Complete Strictly Causal Lorentzian Manifolds

V. M. Gichev·E. A. Meshcheryakov
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Abstract

A flat complete causal Lorentzian manifold is called {\it strictly causal} if the past and the future of each its point are closed near this point. We consider strictly causal manifolds with unipotent holonomy groups and assign to a manifold of this type four nonnegative integers (a signature) and a parabola in the cone of positive definite matrices. Two manifolds are equivalent if and only if their signatures coincides and the corresponding parabolas are equal (up to a suitable automorphism of the cone and an affine change of variable). Also, we give necessary and sufficient conditions, which distinguish parabolas of this type among all parabolas in the cone.

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V. M. Gichev, E. A. Meshcheryakov. 2007-04-05. On Geometry of Flat Complete Strictly Causal Lorentzian Manifolds. https://arxiv.org/abs/math/0509287

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