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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Fold singularities in pseudo-Riemannian geodesic tubes
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by Marek Kossowski PDF
Proc. Amer. Math. Soc. 95 (1985), 463-469 Request permission

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
  • M. Golubitsky and V. Guillemin, Stable mappings and their singularities, Graduate Texts in Mathematics, Vol. 14, Springer-Verlag, New York-Heidelberg, 1973. MR 0341518, DOI 10.1007/978-1-4615-7904-5
  • M. Kossowski, Local differential geometry of transverse metric singularities, Preprint, 1983. —, First order partial differential equations with singular solutions, Preprint, 1984.
  • J. Milnor, Morse theory, Annals of Mathematics Studies, No. 51, Princeton University Press, Princeton, N.J., 1963. Based on lecture notes by M. Spivak and R. Wells. MR 0163331, DOI 10.1515/9781400881802
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Additional Information
  • © Copyright 1985 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 95 (1985), 463-469
  • MSC: Primary 58C27; Secondary 53B20
  • DOI: https://doi.org/10.1090/S0002-9939-1985-0806088-X
  • MathSciNet review: 806088