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• W2051229458 abstract "A complete Riemannian manifold (M,g) is a Ylx-manifold if every unit speed geodesic γ(t) originating at γ(0)=x∈M satisfies γ(l)=x for 0≠l∈R. Bérard-Bergery proved that if (Mm,g),m>1 is a Ylx-manifold, then M is a closed manifold with finite fundamental group, and the cohomology ring H∗(M,Q) is generated by one element. We say that (M,g) is a Yx-manifold if for every ϵ>0 there exists l>ϵ such that for every unit speed geodesic γ(t) originating at x, the point γ(l) is ϵ-close to x. We use Low’s notion of refocussing Lorentzian space–times to show that if (Mm,g),m>1 is a Yx-manifold, then M is a closed manifold with finite fundamental group. As a corollary we get that a Riemannian covering of a Yx-manifold is a Yx-manifold. Another corollary is that if (Mm,g),m=2,3 is a Yx-manifold, then (M,h) is a Ylx-manifold for some metric h." @default.
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• W2051229458 date "2010-10-01" @default.
• W2051229458 modified "2023-09-25" @default.
• W2051229458 title "Topological properties of manifolds admitting a Yx-Riemannian metric" @default.
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• W2051229458 doi "https://doi.org/10.1016/j.geomphys.2010.05.010" @default.
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