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Zbl 1175.53080
Palomo, Francisco J.; Romero, Alfonso
Conformally stationary Lorentzian tori with no conjugate points are flat. (English)
[J] Proc. Am. Math. Soc. 137, No. 7, 2403-2406 (2009). ISSN 0002-9939; ISSN 1088-6826/e

In the paper under review, the authors mainly prove that ``If a conformally stationary Lorentzian torus $(\mathbb{T}^{2},g)$ has no conjugate points along its geodesics, then $(\mathbb{T}^{2},g)$ is flat (Theorem 3.5)". If only the absence of conjugate points on time-like geodesics is assumed then a counterexample is shown. This shows that Theorem 3.5 cannot be generalized under a weaker assumption.
[Cihan Özgür (Balikesir)]

MSC 2000:: *53C50 Lorentz manifolds, manifolds with indefinite metrics
53C22 Geodesics
53C25 Special Riemannian manifolds

Keywords: conformally stationary Lorentzian torus; conjugate points, flat Lorentzian torus

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