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Lorentzian manifolds of nonpositive curvature. II

Author: F. J. Flaherty
Journal: Proc. Amer. Math. Soc. 48 (1975), 199-202
MSC: Primary 53C50
MathSciNet review: 0643823
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Abstract: Suppose that $ M$ is a time oriented, future $ 1$-connected, timelike and null geodesically complete Lorentzian manifold. Previously, we have shown the exponential map at any point of such a manifold embeds the future cone into $ M$ when $ M$ has nonpositive spacetime curvatures. Here we want to demonstrate that under the same hypotheses, $ M$ is homeomorphic to the product of the real line with a Cauchy hypersurface.

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Keywords: Future $ 1$-connected, nonspacelike curves, exponential map, spacetime curvature, globally hyperbolic
Article copyright: © Copyright 1975 American Mathematical Society

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