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

 
 

 

Cut locus contained in a hypersurface


Authors: F. Gómez and M. C. Muñoz
Journal: Proc. Amer. Math. Soc. 104 (1988), 584-586
MSC: Primary 53C20
DOI: https://doi.org/10.1090/S0002-9939-1988-0929429-4
MathSciNet review: 929429
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Abstract: We prove that if the cut locus $ C(p)$ of a point $ p$ in a compact connected Riemannian manifold $ M$ is contained in a connected hypersurface $ N$, then $ M$ is homeomorphic to $ {S^m}$ if $ C(p) \ne N$ and $ M$ is homotopically equivalent to $ {\mathbf{R}}{P^m}$ if $ C(p) = N$.


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DOI: https://doi.org/10.1090/S0002-9939-1988-0929429-4
Article copyright: © Copyright 1988 American Mathematical Society

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