Topological properties of manifolds admitting a -Riemannian metric
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| Title: | Topological properties of manifolds admitting a -Riemannian metric |
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| Authors: | Chernov, Vladimir1 Vladimir.Chernov@dartmouth.edu, Kinlaw, Paul1 Paul.Kinlaw@dartmouth.edu, Sadykov, Rustam2 sadykov@math.toronto.edu |
| Source: | Journal of Geometry & Physics. Oct2010, Vol. 60 Issue 10, p1530-1538. 9p. |
| Subjects: | Topology, Riemannian manifolds, Geodesics, Fundamental groups (Mathematics), Homology theory, Hyperbolic spaces |
| Abstract: | Abstract: A complete Riemannian manifold is a -manifold if every unit speed geodesic originating at satisfies for . Bérard-Bergery proved that if is a -manifold, then is a closed manifold with finite fundamental group, and the cohomology ring is generated by one element. We say that is a -manifold if for every there exists such that for every unit speed geodesic originating at , the point is -close to . We use Low’s notion of refocussing Lorentzian space–times to show that if is a -manifold, then is a closed manifold with finite fundamental group. As a corollary we get that a Riemannian covering of a -manifold is a -manifold. Another corollary is that if is a -manifold, then is a -manifold for some metric . [Copyright &y& Elsevier] |
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| Database: | Engineering Source |
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