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Cited by 27

The DOI matches its Crossref record; 1 of the 1 references it cites were found in a registry or an index.

Transverse, type changing, pseudo riemannian metrics and the extendability of geodesics

Kossowski, Marek, Kriele, Marcus·1994·Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences
DOI 10.1098/rspa.1994.0019
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Abstract

We study the geodesics and pre-geodesics of a smooth manifold with smooth pseudo riemannian metric which changes bilinear type (i. e. the signature changes) on a hypersurface. We classify all geodesics and pre-geodesics that cross the hypersurface of type change transversely. We then apply these results to the eikonal partial differential equation to find geometric conditions for the local existence or non-existence of smooth, transverse solutions.

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Crossref · 10.1098/rspa.1994.0019

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1 of 1 references verified0 citation errors · 0 not checkable

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  • In the Vilenkin-Linde tunneling wave function formalism, the Euclidean action enters with different sign, so probabilities are P ∼ exp(I).

    “In a sense, the Euclidean action enters this formalism with different sign, so that one ends up with probabilities P ∼ exp(I).”

    From Dimensionality, topology, energy, the cosmological constant and signature change (1996) · cites this paper as [31]

Citations

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Research works printed but not linked: 20

  1. Abraham R. & Marsden J. E. 1978 Foundations of mechanics. Addison-Wesley.
  2. 10.1088/0264-9381/10/2/018 · DOI
  3. Dieudonne J. 1960 Foundations of modern analysis. New York: Academic Press.
  4. Dray T., 1991, Particle creation from signature change, Cen. Rel. Crav., 23, 967
  5. Dray T. Manogue C. A. & Tucker R. W. 1993 The scalar field equation in the presence of signature change. Preprint gr-qc/9303002. · DOI
  6. 10.1088/0264-9381/9/6/011 · DOI
  7. 10.1088/0264-9381/9/8/007 · DOI
  8. Hayward S. A. 1993 Junction conditions for signature change. Preprint gr-qc/9303034. · arXiv
  9. Hirsch M. W. Pugh C. C. & Shub M. 1977 Invariant manifolds. In in Mathematics vol. 583. Berlin: Springer-Verlag. · DOI
  10. 10.1088/0264-9381/8/4/007 · DOI
  11. Kossowski M., 1985, Fold singularities in pseudo Riemannian geodesic tubes. Proc. Am math, Soc., 95, 463
  12. Kossowski M., 1987, Pseudo-Riemannian metric singularities and the extendability of parallel transport, Soc., 99, 147
  13. 10.1307/mmj/1029004391 · DOI
  14. 10.1093/qmath/42.1.315 · DOI
  15. 10.1512/iumj.1991.40.40006 · DOI
  16. 10.1088/0264-9381/10/6/012 · DOI
  17. Kossowski M. &Kriele M. 1993c The Einstein equation for signature type changing spacetimes. Preprint.
  18. Kossowski M. & Kriele M. 1993d Characteristic classes for transverse type changing pseudo Riemannian manifolds. Preprint.
  19. 10.1016/0393-0440(92)90023-T · DOI
  20. Vanderbauwhede A. 1989 Centre manifolds normal forms and elementary bifurcations. In Dynamics reported vol. 2 (ed. U. Kirchgraber & H. O. Walther). John Wiley and B. G. Teubner. · DOI

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Metadata

Authors
Kossowski, M., & Kriele, M.
Venue
Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences
Publisher
The Royal Society
Published
1994-02-08
Volume
444
Issue
1921
Pages
297-306
ISSN
  • 0962-8444
  • 2053-9177
DOI
10.1098/rspa.1994.0019
Cited by
27
References
1
Language
en
Licence
royalsociety.org/journals/ethics-policies/data-sharing-mining/ (tdm)

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