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)

 
 

 

Decomposition of cut loci


Author: Richard L. Bishop
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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 53C20, 57D70

Retrieve articles in all journals with MSC: 53C20, 57D70


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1977-0478066-X
Keywords: Riemannian geometry, cut locus, conjugate locus
Article copyright: © Copyright 1977 American Mathematical Society

American Mathematical Society