Existence and multiplicity of normal geodesics in Lorentzian manifolds

Journal of Geometric Analysis

Volumn 10, Issue 4, 2000, Pages 623-651

  Candela, A M ^a   Masiello, A ^a   Salvatore, A ^a  

^a UNIVERSITY OF BARI   (Italy)

Author keywords

Lorentzian manifolds; normal geodesics; relative category; saddle points

Indexed keywords

EID: 0000163867     PISSN: 10506926     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02921989     Document Type: Article

References (23)

1. Beem, J.K.; Ehrlich, P.E.; Easley, K.L.Global Lorentzian Geometry, Monographs Textbooks Pure Appl. Math.;202, Dekker Inc.; New York, 1996.
2. V. Benci D. Fortunato 1994 On the existence of infinitely many geodesics on space-time manifolds Adv. Math. 105 1 25 10.1006/aima.1994.1036 1275190 0808.58016
3. V. Benci D. Fortunato F. Giannoni 1991 On the existence of multiple geodesics in static space-times Ann. Inst. H. Poincaré Anal. Non Linéaire 8 79 102 1094653 0716.53057
4. V. Benci D. Fortunalo A. Masiello 1994 On the geodesic connecledeness of Lorentzian manifolds Math. Z. 217 73 93 10.1007/BF02571935 1292174 0807.53054
5. A.M. Candela F. Giannoni A. Masiello 1999 Multiple critical points for indefinite functional and applications J. Differential Equations 155 203 230 10.1006/jdeq.1998.3572 1693194 0932.58012
6. A.M. Candela A. Salvatore 1997 Light rays joining two submanifolds in space-times J. Geom. Phys. 22 281 297 10.1016/S0393-0440(96)00034-4 1454492 0880.58005
7. Fadell, E. Lectures in cohomological index theories of G-spaces with applications to critical point theory, Raccolta di seminari, Università della Calabria, 1985.
8. E. Fadell S. Husseini 1991 Category of loop spaces of open subsets in Euclidean space Nonlinear Anal. TMA 17 1153 1161 10.1016/0362-546X(91)90234-R 1137900 0756.55008
9. E. Fadell S. Husseini 1994 Relative category, products and coproducls Rend. Sem. Mat. Fis. Univ. Milano LXIV 99 117 1397466
10. Fournier, G.; Lupo, D.; Ramos, M.; Willem, M. Limit relative category and critical point theory, inDynamics Reported,III, Springer-Verlag, Berlin, 1994.
11. Fournier, G. and Willem, M. Relative category and the calculus of variations, inVariational Problems, Beresticky, H.; Coron, J.M.; Ekeland, I.; Eds.; Birkhäuser, Basel, 95-104, 1990.
12. R. Geroch 1970 Domains of dependence J. Math. Phys. 11 437 449 10.1063/1.1665157 270697 0189.27602
13. F. Giannoni A. Masiello 1995 Geodesies on product Lorentzian manifolds Ann. Inst. H. Poincaré Anal. Non Linéaire 12 27 60 1320567 0839.53046
14. K. Grove 1973 Condition (C) for the energy integral on certain path spaces and applications to the theory of geodesies J. Differential Geom. 8 207 223 339270 0277.58004
15. Hawking, S.W. and Ellis, G.F.R.The Large Scale Structure of Space-Time, Cambridge University Press, London, 1973.
16. Klingenberg, W.Riemannian Geometry, de Gruyter, Berlin, 1982.
17. Masiello, A.Variational Methods in Lorentzian Geometry, Pitman Res. Notes Math. Ser.;309, Longman Sci. Tech.; Harlow, 1994.
18. J. Molina 1996 Existence and multiplicity of normal geodesies on static space-time manifolds Bollettino U.M.I. 10-A 7 305 318 1405246
19. O'Neill, B.Semi-Riemannian Geometry with Applications to Relativity, Academic Press, New York, 1983.
20. R.S. Palais 1963 Morse Theory on Hilbert manifolds Topology 2 299 340 10.1016/0040-9383(63)90013-2 158410 0122.10702
21. Rabinowitz, P.H. Minimax methods in critical point theory with applications to differential equations,CBMS Reg. Conf. Series Math.; Am. Math. Soc.;65, (1986).
22. A. Salvatore 1996 Trajectories of dynamical systems joining two given submanifolds Differential Integral Equations 9 779 790 1401437 0853.58033
23. A. Szulkin 1990 A relative category and applications to critical point theory for strongly indefinite functionals Nonlinear Anal. TMA 15 725 739 10.1016/0362-546X(90)90089-Y 1074951 0719.58011