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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Fold singularities in pseudo-Riemannian geodesic tubes


Author: Marek Kossowski
Journal: Proc. Amer. Math. Soc. 95 (1985), 463-469
MSC: Primary 58C27; Secondary 53B20
MathSciNet review: 806088
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Abstract | References | Similar Articles | Additional Information

Abstract: For a general submanifold of a pseudo Riemannian manifold, the exponential mapping of the orthogonal bundle into the ambient manifold may fail to be a diffeomorphism on the zero section. Here we show that differential geometric information intrinsic to the submanifold determines when this map has a fold singularity.


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

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  • [2] M. Kossowski, Local differential geometry of transverse metric singularities, Preprint, 1983.
  • [3] -, First order partial differential equations with singular solutions, Preprint, 1984.
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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1985-0806088-X
PII: S 0002-9939(1985)0806088-X
Keywords: Pseudo Riemannian manifold, singular metric, geodesic tube, fold singularity
Article copyright: © Copyright 1985 American Mathematical Society