On Geometry of Flat Complete Strictly Causal Lorentzian Manifolds

Details On Geometry of Flat Complete Strictly Causal Lorentzian Manifolds On Geometry of Flat Complete Strictly Causal Lorentzian Manifolds

2005-09-13

arxiv.org/abs/math/0509287v2

Siberian Math. J., v. 48, no. 1, pp. 62-72, 2007

Mathematics

Metric Geometry

The exposition is revised (no essential change in the content). The paper is published

Scientific paper

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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