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Proceedings of the American Mathematical Society

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Decomposition of cut loci

Author: Richard L. Bishop
Journal: Proc. Amer. Math. Soc. 65 (1977), 133-136
MSC: Primary 53C20; Secondary 57D70
MathSciNet review: 0478066
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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 [Enhancements On Off] (What's this?)

  • [1] R. L. Bishop and R. J. Crittenden, Geometry of manifolds, Academic Press, New York, 1964. MR 29 #6401 MR 0169148 (29:6401)
  • [2] H. Gluck and D. Singer, Deformations of geodesic fields, Bull Amer. Math. Soc. 82 (1976), 571-574. MR 0415538 (54:3624)
  • [3] F. W. Warner, The conjugate locus of a Riemannian manifold, American J. Math. 87 (1965), 575-604. MR 34 #8344 MR 0208534 (34:8344)

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Keywords: Riemannian geometry, cut locus, conjugate locus
Article copyright: © Copyright 1977 American Mathematical Society

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