Advertisement

Multiplicity of Timelike Geodesics in Splitting Lorentzian Manifolds

  • A. M. Candela
Conference paper

Abstract

In the theory of General Relativity models of gravitational fields are particular examples of Lorentzian manifolds, the so-called space-times, and the trajectory of a free falling particle on which only gravity acts is just a timelike geodesic in such a manifold [1,2].

Keywords

Critical Point Theory Galerkin Approximation Lorentzian Manifold Relative Category Periodic Trajectory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Beem J.K., Ehrlich P.E., Easley K.L. (1996): Global Lorentzian Geometry. Monographs Textbooks Pure Appl. Math. 202, Dekker, New YorkMATHGoogle Scholar
  2. 2.
    Hawking S.W., Ellis G.F.R. (1973): The Large Scale Structure of Space-Time. Cambridge University Press, CambridgeMATHCrossRefGoogle Scholar
  3. 3.
    Candela A.M., Giannoni F., Masiello A.: Multiple critical points for indefinite functionals and applications. J. Differential Equations, to appearGoogle Scholar
  4. 4.
    O’Neill B. (1983): Semi-Riemannian Geometry with Applications to Relativity. Academic Press Inc., New YorkMATHGoogle Scholar
  5. 5.
    Greco C. (1990): Periodic trajectories for a class of Lorentz metrics of a time-dependent gravitational field. Math. Ann. 287, 515–521MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Masiello A. (1995): On the existence of a timelike trajectory for a Lorentzian metric. Proc. Roy. Soc. Edinburgh A 125, 807–815MathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    Candela A.M., Masiello A., Salvatore A.: Existence and multiplicity of normal geodesies in Lorentzian manifolds. J. Geom. Anal, to appearGoogle Scholar
  8. 8.
    Benci V., Fortunato D., Masiello A. (1994): On the geodesic connectedness of Lorentzian manifolds. Math. Z. 217, 73–93MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    Giannoni F, Masiello A. (1995): Geodesies on product Lorentzian manifolds. Ann. Inst. H. Poincaré Anal. Non Linéaire 12, 27–60MathSciNetMATHGoogle Scholar
  10. 10.
    Masiello A. (1994): Variational Methods in Lorentzian Geometry. Pitman Res. Notes Math. Ser. 309, Longman Sci. Tech., HarlowGoogle Scholar
  11. 11.
    Klingenberg W. (1978): Lectures on Closed Geodesies. Springer, BerlinCrossRefGoogle Scholar
  12. 12.
    Klingenberg W. (1982) Riemannian Geometry, de Gruyter, BerlinMATHGoogle Scholar
  13. 13.
    Fadell E. (1985): Lectures in cohomological index theories of G-spaces with applications to critical point theory. Raccolta di seminari, Università della CalabriaGoogle Scholar
  14. 14.
    Fournier G., Willem M. (1990): Relative category and the calculus of variations, in Variational problems, ed. by H. Beresticky, J.M. Coron, I. Ekeland, Birkhäuser, Basel, pp. 95–104Google Scholar
  15. 15.
    Szulkin A. (1990): A relative category and applications to critical point theory for strongly indefinite functionals, Nonlinear Anal. TMA 15, 725–739MathSciNetMATHGoogle Scholar
  16. 16.
    Palais R.S. (1966): Lusternik-Schnirelman theory on Banach manifolds. Topology 5, 115–132MathSciNetMATHCrossRefGoogle Scholar
  17. 17.
    Fadell E., Husseini S. (1991 ): Category of loop spaces of open subsets in Euclidean space. Nonlinear Anal. TMA 17, 1153–1161MathSciNetMATHCrossRefGoogle Scholar
  18. 18.
    Fadell E., Husseini S. (1994): Relative category, products and coproducts. Rend. Sem. Mat. Fis. Univ. Milano LXIV, 99–117MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Italia 2000

Authors and Affiliations

  • A. M. Candela

There are no affiliations available

Personalised recommendations