{"paper":{"title":"Topological properties of manifolds admitting a $Y^x$-Riemannian metric","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","math-ph","math.GT","math.MP"],"primary_cat":"math.DG","authors_text":"Paul Kinlaw, Rustam Sadykov, Vladimir Chernov","submitted_at":"2010-05-27T14:07:52Z","abstract_excerpt":"A complete Riemannian manifold $(M, g)$ is a $Y^x_l$-manifold if every unit speed geodesic $\\gamma(t)$ originating at $\\gamma(0)=x\\in M$ satisfies $\\gamma(l)=x$ for $0\\neq l\\in \\R$. B\\'erard-Bergery proved that if $(M^m,g), m>1$ is a $Y^x_l$-manifold, then $M$ is a closed manifold with finite fundamental group, and the cohomology ring $H^*(M, \\Q)$ is generated by one element.\n  We say that $(M,g)$ is a $Y^x$-manifold if for every $\\epsilon >0$ there exists $l>\\epsilon$ such that for every unit speed geodesic $\\gamma(t)$ originating at $x$, the point $\\gamma(l)$ is $\\epsilon$-close to $x$. We u"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.5075","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}