Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF Free Access

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?)

  • M. Golubitsky and V. Guillemin, Stable mappings and their singularities, Springer-Verlag, New York-Heidelberg, 1973. Graduate Texts in Mathematics, Vol. 14. MR 0341518
  • 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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 58C27, 53B20

Retrieve articles in all journals with MSC: 58C27, 53B20

Additional Information

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