Cut locus contained in a hypersurface

Gómez, F.; Muñoz, M. C.

doi:10.1090/S0002-9939-1988-0929429-4

Cut locus contained in a hypersurface
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by F. Gómez and M. C. Muñoz PDF

Proc. Amer. Math. Soc. 104 (1988), 584-586 Request permission

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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