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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Lorentzian manifolds of nonpositive curvature. II


Author: F. J. Flaherty
Journal: Proc. Amer. Math. Soc. 48 (1975), 199-202
MSC: Primary 53C50
DOI: https://doi.org/10.1090/S0002-9939-1975-0643823-1
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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DOI: https://doi.org/10.1090/S0002-9939-1975-0643823-1
Keywords: Future $ 1$-connected, nonspacelike curves, exponential map, spacetime curvature, globally hyperbolic
Article copyright: © Copyright 1975 American Mathematical Society