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
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