Timelike periodic trajectories in spatially compact lorentz manifolds

Proceedings of the American Mathematical Society

Volumn 127, Issue 10, 1999, Pages 3057-3066

  Sánchez, Miguel ^a  

^a UNIVERSITY OF GRANADA   (Spain)

Author keywords

Causality; Closed geodesic; Compact lorentz manifold; Periodic trajectory; Stationary manifold

Indexed keywords

EID: 22844455839     PISSN: 00029939     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9939-99-04979-5     Document Type: Article

References (24)

1. V. Bench Periodic solutions of Lagrangian systems on a compact manifold, J. Diff. Eq. 63 (1986) 135-161. MR 88h:58102
2. J.K. Beem, P.E. Ehrlich: "Global Lorentzian Geometry", Pure and Applied Mathematics, Marcel Dekker Inc., NY, 1981.
3. V. Benci, D. Fortunato: Periodic trajectories for the Lorentz metric of a static gravitational field, Proc. on "Variational Methods" (H. Berestycki- J.M. Coron- I. Ekeland, Ed.) Paris (1988) 413-429.
4. V. Benci, D. Fortunato, F. Giannoni: On the existence of multiple geodesies in static space-times, Ann. Inst. Henri Poin. 8 (1991) 79-102. MR 91m:58027
5. V. Benci, D. Fortunato, F. Giannoni: On the existence of periodic trajectories in static Lorentzian manifolds with singular boundary, Nonlinear Analysis, a tribute in honour of Giovanni Prodi, Pisa (1991) 109-133.
6. R. Bartolo, A. Masiello: On the existence of infinitely many trajectories for a class of Lorentzian manifolds like Schwarzschild and Reissner-Nordström spacetimes, J. Math. Anal. Appl. 199 (1996) 14-38. MR 98b:58036
7. A.M. Candela: Lightlike periodic trajectories in space-times, Ann. Mat. Pura Appl., CLXXI (1996) 131-158. MR 98c:58026
8. G.J. Galloway: Closed timelike geodesies, Trans. Amer. Math. Soc. 285 (1984) 379-388. MR 85k:53061
9. G.J. Galloway: Compact Lorentzian manifolds without closed non spacelike geodesies, Proc. Amer. Math. Soc. 98 (1986) 119-123. MR 87i:53094
10. R.P. Geroch: Domain of dependence, J. Math. Phys. 11 (1970) 437-449.
11. F. Giannoni, A. Masiello: On the existence of geodesies on stationary Lorentz manifolds with convex boundary, J. Func. Anal. 101 No. 2 (1991) 340-369. MR 92k:58053
12. C. Greco: Periodic trajectories in static space-times, Proc. Roy. Soc. Edinb. 113A (1989) 99-103. MR 91e:53043
13. C. Greco: Multiple periodic trajectories for a class of Lorentz metrics of a time-dependent gravitational field, Math. Ann. 287 (1990) 515-521. MR 91d:58045
14. A. Masiello: Timelike periodic trajectories in stationary Lorentz manifolds, Nonlinear Anal. TMA, 19 (1992) 531-545.
15. A. Masiello: On the existence of a timelike trajectory for a Lorentzian metric, Proc. Roy. Soc. Edinb. 125A (1995) 807-815. MR 96j:58037
16. A. Masiello, P. Piccione: Shortening null geodesies in Lorentzian manifolds. Applications to closed light rays, Differential Geom. Appl. 8 (1998) 47-70. CMP 98:07
17. A. Masiello, L. Pisani: Existence of a time-like periodic trajectory for a time-dependent Lorentz metric, Ann. Univ. Ferrara - Sc. Mat. XXXVI (1990) 207-222.
18. B. O'Neill: "Semi-Riemannian Geometry", Academic Press, San Diego, CA, 1983. MR 85f:53002
19. M. Sánchez: Structure of Lorentzian tori admitting a Killing vector field, Trans. Amer. Math. Soc. 349 No. 3 (1997) 1063-1080. MR 97f:53108
20. M. Sánchez: Geodesies in static spacetimes and t-periodic trajectories, Nonlinear Anal. TMA, 35 (1999) 677-686.
21. M. Sánchez: Some remarks on Causality and Variational Methods in Lorentzian Manifolds, Conf. Sem. Mat. Univ. Bari 265 (1997). CMP 98:09
22. M. Sánchez: Lorentzian manifolds admitting a Killing vector field, Nonlinear Anal. TMA 30 No. 1 (1997) 643-654.
23. R.K. Sachs, H. Wu, "General Relativity for Mathematicians", Grad. Texts in Math. 48, Springer-Verlag, NY (1977). MR 58:20239a
24. F.J. Tipler: Existence of a closed timelike geodesic in Lorentz spaces, Proc. Amer. Math. Soc. 76 No. 1 (1979) 145-147. MR 80f:83016