Decomposition of cut loci
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- by Richard L. Bishop PDF
- Proc. Amer. Math. Soc. 65 (1977), 133-136 Request permission
Abstract:
If p is a point in a complete riemannian manifold, the points of the cut locus of p are designated as singular or ordinary according to whether there is just one or more minimizing geodesics from p. It is proved that the ordinary cut-points are dense in the cut locus.References
- Richard L. Bishop and Richard J. Crittenden, Geometry of manifolds, Pure and Applied Mathematics, Vol. XV, Academic Press, New York-London, 1964. MR 0169148
- Herman Gluck and David Singer, Deformations of geodesic fields, Bull. Amer. Math. Soc. 82 (1976), no. 4, 571–574. MR 415538, DOI 10.1090/S0002-9904-1976-14107-9
- Frank W. Warner, The conjugate locus of a Riemannian manifold, Amer. J. Math. 87 (1965), 575–604. MR 208534, DOI 10.2307/2373064
Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 65 (1977), 133-136
- MSC: Primary 53C20; Secondary 57D70
- DOI: https://doi.org/10.1090/S0002-9939-1977-0478066-X
- MathSciNet review: 0478066