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Proceedings of the American Mathematical Society

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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: 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?)

  • [1] M. Golubitsky and V. Guillemin, Stable mappings and their singularities, Graduate Texts in Math., no. 14, Springer-Verlag, Berlin and New York, 1973. MR 0341518 (49:6269)
  • [2] M. Kossowski, Local differential geometry of transverse metric singularities, Preprint, 1983.
  • [3] -, First order partial differential equations with singular solutions, Preprint, 1984.
  • [4] J. Milnor, Morse theory, Ann. of Math. Stud., no. 61, Princeton Univ. Press, Princeton, N. J., 1973. MR 0163331 (29:634)

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Keywords: Pseudo Riemannian manifold, singular metric, geodesic tube, fold singularity
Article copyright: © Copyright 1985 American Mathematical Society

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