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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
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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.


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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