On the existence of multiple geodesics in static space-times

 Access to full text

 Full (PDF)

1. [1] S.I. Alber, The Topology of Functional Manifolds and the Calculus of Variations in the Large, Russian Math. Surv., Vol. 25, 1970, p. 51-117. Zbl0222.58002MR279832
2. [2] A. Avez, Essais de géométrie Riemanniene hyperbolique: Applications to the relativité générale, Inst. Fourier, Vol. 132, 1963, p. 105-190. Zbl0188.54801MR167940
3. [3] P. Bartolo, V. Benci, and D. Fortunato, Abstract Critical Point Theorems and Applications to Some Nonlinear Problems with "Strong Resonance" at Infinity,Nonlinear Anal. T.M.A., Vol. 7, 1983, pp. 981-1012. Zbl0522.58012MR713209
4. [4] J.K. Beem and P. Erlich, Global LorentzianGeometry, M. Dekker, Pure Appl. Math., Vol. 67, 1981. Zbl0462.53001MR619853
5. [5] V. Benci, Periodic Solutions of Lagrangian Systems on Compact Manifold, J. Diff. Eq., Vol. 63, 1986, pp. 135-161. Zbl0605.58034MR848265
6. [6] V. Benci and D. Fortunato, Existence of Geodesics for the Lorentz Metric of a Stationary Gravitational Field, Ann. Inst. H. Poincaré, Anal. non linéaire, Vol. 7, 1990, pp. 27-35. Zbl0697.58011MR1046082
7. [7] V. Benci and D. Fortunato, Periodic Trajectories for the Lorentz Metric of a Static Gravitational Field, Proc. on "Variational Problems", Paris, June 1988 (to appear). Zbl0719.58009MR1205170
8. [8] V. Benci and D. Fortunato, On the Existence of Infinitely Many Geodesics on Space-Time Manifolds, preprint, Dip. Mat. Univ.Bari, 1989. Zbl0808.58016MR1275190
9. [9] V. Benci, D. Fortunato and F. Giannoni, On the Existence of Geodesics in Static Lorentz Manifolds with Nonsmooth Boundary, preprint. Ist. Mat. Appl. Univ.Pisa. Zbl0737.53059
10. [10] A. Canino, On p-convex Sets and Geodesics, J. Diff. Eq., Vol. 75, 1988, pp. 118-157. Zbl0661.34042MR957011
11. [11] G. Galloway, Closed Timelike Geodesics, Trans. Am. Math. Soc., Vol. 285, 1984, pp. 379-388. Zbl0547.53033MR748844
12. [12] G. Galloway, Compact Lorentzian Manifolds Without Closed Nonspacelike Geodesics, Proc. Am. Math. Soc., Vol. 98, 1986, pp. 119-124. Zbl0601.53053MR848888
13. [13] C. Greco, Periodic Trajectories for a Class of Lorentz Metrics of a Time-Dependent Gravitational Field, preprint, Dip. Mat. Univ.Bari, 1989. MR1060690
14. [14] C. Greco, Periodic Trajectories in Static Space-Times, preprint, Dip. Mat. Univ.Bari, 1989. Zbl0691.53052MR1025457
15. [15] S.W. Hawking and G.F. Ellis, The Large Scale Structure of Space Time, Cambridge Univ. Press, 1973. Zbl0265.53054MR424186
16. [16] J. Milnor, Morse Theory, Ann. Math. Studies, Vol. 51, Princeton Univ. Press, 1963. Zbl0108.10401
17. [17] J. Nash, The Embedding Problem for Riemannian Manifolds, Ann. Math., Vol. 63, 1956, pp. 20-63. Zbl0070.38603MR75639
18. [18] B. O'Neil, Semi-Riemannian Geometry with Applications to relativity, Academic Press Inc., New York-London, 1983. Zbl0531.53051
19. [19] R.S. Palais, Critical Point Theory and the Minimax Principle, Global Anal., Proc. Sym. "Pure Math.", Vol. 15, Amer. Math. Soc., 1970, pp. 185-202. Zbl0212.28902MR264712
20. [20] R.S. Palais, Morse Theory on Hilbert Manifolds, Topology, Vol. 22, 1963, pp. 299- 340. Zbl0122.10702MR158410
21. [21] R. Penrose, Techniques of Differential Topology in Relativity, Conf. Board Math. Sci., Vol. 7, S.I.A.M., Philadelphia, 1972. Zbl0321.53001MR469146
22. [22] P.H. Rabinovitz, Minimax Methods in Critical Point Theory with Applications to Differential Equations, Reg. Conf. Series, Am. Math. Soc., Vol. 65, 1986. Zbl0609.58002MR845785
23. [23] J.T. Schwartz, Nonlinear Functional Analysis, Gordon and Breach, New York, 1969. Zbl0203.14501MR433481
24. [24] H.J. Seifert, Global Connectivity by Time-Like Geodesics, Z. Natureforsch, Vol. 22 a, 1970, pp. 1356-1360. Zbl0163.43701MR225556
25. [25] J.P. Serre, Homologie singulière des espaces fibres, Ann. Math., Vol. 54, 1951, pp. 425- 505. Zbl0045.26003MR45386
26. [26] F. Tripler, Existence of Closed Time-Like Geodesics in Lorentz Spaces, Proc. Am. Math. Soc., Vol. 76, 1979, pp. 145-147. Zbl0387.53024
27. [27] K. Uhlenbeck, A Morse Theory for Geodesics on a Lorentz Manifold, Topology, Vol. 14, 1975, pp. 69-90. Zbl0323.58010MR383461
28. [28] M. Vigue-Poirier and D. Sullivan, The Homology Theory of the Closed Geodesic Problem, J. Diff. Geom., Vol. 11, 1979, pp. 633-644. Zbl0361.53058MR455028

1. Carlo Greco, The Dirichlet-problem for harmonic maps from the disk into a lorentzian warped product
2. Vieri Benci, Donato Fortunato, Fabio Giannoni, Some results on the existence of geodesics in static Lorentz manifolds with singular boundary
3. Carlo Greco, Infinitely many spacelike periodic trajectories on a class of Lorentz manifolds
4. V. Benci, D. Fortunato, F. Giannoni, On the existence of geodesics in static Lorentz manifolds with singular boundary
5. Miguel Sánchez, An introduction to the completeness of compact semi-riemannian manifolds