Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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
MathSciNet review: 929429
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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$.

References [Enhancements On Off] (What's this?)

  • [1] Arthur L. Besse, Manifolds all of whose geodesics are closed, Ergebnisse der Mathematik und ihrer Grenzgebiete [Results in Mathematics and Related Areas], vol. 93, Springer-Verlag, Berlin-New York, 1978. With appendices by D. B. A. Epstein, J.-P. Bourguignon, L. Bérard-Bergery, M. Berger and J. L. Kazdan. MR 496885
  • [2] S. López de Medrano, Involutions on manifolds, Springer-Verlag, New York-Heidelberg, 1971. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 59. MR 0298698
  • [3] J. Milnor, Differential topology, Lectures on Modern Mathematics, Vol. II, Wiley, New York, 1964, pp. 165–183. MR 0178474
  • [4] Edwin H. Spanier, Algebraic topology, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1966. MR 0210112

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 53C20

Retrieve articles in all journals with MSC: 53C20

Additional Information

Article copyright: © Copyright 1988 American Mathematical Society

American Mathematical Society