An introduction to the completeness of compact semi-riemannian manifolds
Séminaire de théorie spectrale et géométrie, Volume 13 (1994-1995), pp. 37-53.
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     url = {http://www.numdam.org/item/TSG_1994-1995__13__37_0/}
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Sánchez, Miguel. An introduction to the completeness of compact semi-riemannian manifolds. Séminaire de théorie spectrale et géométrie, Volume 13 (1994-1995), pp. 37-53. http://www.numdam.org/item/TSG_1994-1995__13__37_0/

[ARS] L.J. Alias, A. Romero, M. Sánchez. _ Uniqueness of complete spacelike hypersurfaces of constant mean curvature in generalized Robertson-Walker spacetimes, Gen. Rel. Grav. 27 ( 1995), 71-84. | MR | Zbl

[Be1] J.K. Beem. _ Some examples of incomplete spacetimes, Gen. Rel. Grav. 7 ( 1976), 501-509. | Zbl

[Be2] J.K. Beem. _ Disprisoning and pseudoconvex manifolds, Proceedings Symp. PureMath. 54 ( 1993), 19-26. | MR | Zbl

[BeEh] J.K. Beem, P.E. Ehrlich. _ Geodesic completeness and stability, Math. Proc. Camb. Phil. Soc. 102 ( 1987), 319-328. | MR | Zbl

[BePa1] J.K. Beem, P.E. Parker. _ The space of geodesics, Geom. Dedicata 38 ( 1991), 87-99. | MR | Zbl

[BePa2] J.K. Beem, P.E. Parker. _ Whitney stability of solvability, Pac. J. Math. 116 ( 1985), 11-23. | MR | Zbl

[BFG] V. Benci, D. Fortunato, F. Giannoni. _ On the existence of multiple geodesics in static space-times, Ann. Inst. Henri Poincaré 81, n°l ( 1991), 79-102. | Numdam | MR | Zbl

[BFM] V. Benci, D. Fortunato, A. Masiello. _ On the geodesic connectedeness of Lorentzian manifolds, Math. Z. 217 ( 1994), 73-93. | MR | Zbl

[Ca] Y. Carrière. _ Autour de la conjecture de L. Markus sur les variétés affines, Invent. Math. 95 ( 1989), 615-628. | MR | Zbl

[CaRo] Y. Carrière, L. Rozoy. _ Complétude des métriques lorentziennes de T2 et difféomorphismes du cercle, Bol. Soc. Bras. Mat 25 ( 1994), 223-235. | MR | Zbl

[CI] C.J.S. Clarke. _ On the geodesic completeness of causal space-times, Proc. Cam. Phil. Soc. 69 ( 1971), 319-324. | MR | Zbl

[CoTu1] A.A. Coley, B.O.J. Tupper. _ Special conformal Killing vector space-times and symmetry inheritance, J. Math. Phys. 30 ( 1989), 2616-2625. | MR | Zbl

[CoTu2] A.A. Coley, B.O.J. Tupper. _ Space-times admitting special affine conformai vectors, J. Math. Phys. 31 ( 1990), 649-652. | MR | Zbl

[Dulh] D. Duncan, E. Ihrig. _ Incomplete flat homogeneous geometries, Proceedings Symp. PureMath. 54 Part 2 ( 1993), 197-202. | MR | Zbl

[EIMM] D. Eardley,J. Isenberg, J. Marsden, V. Moncrief. _ Homothetic and conformal symmetries of solutions to Einstein's equations, Commun. Math. Phys. 106 ( 1987), 137-158. | MR | Zbl

[EISc] G.F.R. Ellis, B.G. Schmidt. _ Singulars pace-times, Gen. Rel. Grav. 7 ( 1977),915-953. | MR | Zbl

[FaKr] H.M. Farkas, I. Kra _ Riemann Surfaces, GraduateTexts in Mathematics, Springer-Verlag, N.Y. Inc., 1992. | MR | Zbl

[FGH] D. Fried, W. Goldman, M. Hirsch. _ Affine manifolds with nilpotent holonomy, Comment Math. Helv. 56 ( 1975), 487-499. | MR | Zbl

[FMNEKTY] J. Friedman, M.S. Morris, I.D. Novikov, F. Echevarría, G. Klinkhammer, K.S. Thorne, U. Yurtsever. _ Cauchy problem in spacetimes with a closed timelike curve, Phys. Rev. D 42 ( 1990),1915-1930. | MR

[FrNo] V.P. Frolov, I.D. Novikov. _ Physical effects in wormholes and time machines, Phys. Rev. D 42 ( 1990), 1057-1065. | MR

[FrSc] H. Friedrich, B.G. Schmidt. _ Conformal geodesics in generai relativity, Proc. R. Soc. Lond. A 414 ( 1987), 171-195. | MR | Zbl

[FuAr] P.M.D. Furness, D.K. Arrowsmith. _ Locally symmetrie spaces, J. London Math. Soc. 10 ( 1975), 487-499. | MR | Zbl

[FuFe] P.M.D. Furness, E. Fedida. _ Sur les structures pseudo-riemanniennes plates des variétés compactes, I. Nigerian Math. Soc. 5 ( 1986), 63-77. | MR | Zbl

[Ga] G.J. Galloway. _ Compact Lorentzian manifolds without closed non spacelike geodesics, Proc. Amer. Math. Soc. 98 ( 1986), 119-123. | MR | Zbl

[Ge] R.P. Geroch. _ What is a singularity hi General Relativity?, Ann. Phys. 48 ( 1968), 526-540. | Zbl

[Gi] F. Giannoni. _ Geodesics on non static Lorentz manifolds of Reissner-Nordström type, Math. Ann. 291 ( 1991), 383-401. | MR | Zbl

[GiMa] F. Giannoni, A. Massiello. _ Geodesics on Lorentzian manifolds with quasi-convex boundary, Manuscripta Math. 78 ( 1993), 381-396. | MR | Zbl

(GoHi] W.M. Goldman, M. Hirsch. _ Affine manifolds and orbits of algebraic groups, Trans. Amer. Math. Soc. 295 ( 1986), 175-198. | MR | Zbl

[GuLa] M. Guediri, J. Lafontaine. _ Sur le complétude des variétés pseudo-riemannienne, to appear in J. Geo m. Phys.. | Zbl

[HaEl] S.W. Hawking, G.F.R. Ellis. _ The large scale structure of space time, Cambridge Monographs in Mathematical Physics, Cambridge Univ. Press, 1973. | MR | Zbl

[Har] S.G. Harris. _ Conformally stationary spacetimes, Class. Quantum Grav., 1992,1823-1827. | MR | Zbl

[Haw] S.W. Hawking. _ The chronology protection conjecture, Phys. Rev. D 46 ( 1992), 603-611. | MR

[Ka] Y. Kamishima. _ Completeness of Lorentz manifolds of constant curvature admitting Kiilingvector fields, J. Differential Geometry 37 ( 1993), 569-601. | MR | Zbl

[KoNo] S. Kobayashi, K. Nomizu. _ Foundations of differential geometry, vol. 1, Wiley Inters. N.Y, 1963. | MR | Zbl

[Kul] R.S. Kulkarni._ An analogue to the Riemann mapping theorem for Lorentz metrics, Proc. Royal Soc. London 401 ( 1985), 117-130. | MR | Zbl

[Kun] W. Kundt. _ Note on the completeness of spacetimes, Zs. f. Phys. 172 ( 1963), 488-489. | MR | Zbl

[La] J. Lafuente Löpez. _ A geodesic completeness theorem for locally symmetrie Lorentz manifolds, Rev. Mat. Univ. Complutense Madrid 1 ( 1988), 101-110. | MR | Zbl

[Lo] R.J. Low. _ The geometry of the space of null geodesics, J. Math. Phys. 30 ( 1989), 809-811. | MR | Zbl

[Ma] J.E. Marsden. _ On completeness of homogeneous pseudo-Riemannian manifolds, Indiana Univ. Math. J. 22 ( 1973), 1065-1066. | MR | Zbl

[NoOz] K. Nomizu, H. Ozeki. _ The existence of complete Riemannian metrics, Proc. Amer. Math. Soc. 12 ( 1961), 889-891. | MR | Zbl

[On] B. O'Neill. _ Semi-Riemannian geometry with applications to relativity, Academic Press, N.Y, 1983. | MR | Zbl

[RoSa1] A. Romero, M. Sánchez. _ On the completeness of geodesics obtained as a limit, J. Math. Phys. 341 n°8 ( 1993), 3768-3774. | MR | Zbl

[RoSa2] A. Romero, M. Sànchez. _ New properties and examples of incomplete Lorentzian tori, J. Math. Phys. 35 n°4 ( 1994), 1992-1997. | MR | Zbl

[RoSa3] A. Romero, M. Sànchez. _ On the completeness of certain families of semi-Riemannian manifolds, Geom. Dedicata 53 ( 1994), 103-117. | MR | Zbl

[RoSa4] A. Romero, M. Sànchez. _ Completeness of compact Lorentz manifolds admitting a time like conformal Killling vector field, to appear in Proc. Amer. Math. Soc. | MR | Zbl

[RoSa5] A. Romero, M. Sànchez. _ On completeness of compact Lorentzian manifolds, Series on Geometry and Topology, Vol. 6, World Scientific Publishing Co., 1994. | MR | Zbl

[RoSa6] A. Romero, M. Sànchez. _ An integral inequality on compact Lorentz manifolds and its applications, to appear in Bull. London Math. Soc. | MR | Zbl

[Sa1] M. Sànchez. _ Completitud geodésica de variedades compactas semi-riemannianas, Tesis Doctoral, Granada, Mayo 1994.

[Sa2] M. Sànchez. _ Structure of Lorentzion ton with a küling vector field, preprint, Universidad de Granada, 1995.

[Sa3] M. Sànchez. _ A new Avez-Seifert type resùlt for geodesics in generalized Reissner-Nordström spacetimes, preprint, Universidad de Granada, 1995.

[SaWu] R.K. Sachs, H. Wu. _ General Relativity for Mathematicians, Graduate Texts in Mathematics, Springer-Verlag, N.Y. Inc., 1977. | MR | Zbl

[Se] H.J. Seifert. _ The causal boundary of space-times, Gen. Rel. Grav. 1 ( 1971), 247-259. | MR | Zbl

[Yu] U. Yurtsever. _ Test üelds on compact space-times, J. Math. Phys. 31 ( 1990), 3064-3078. | MR | Zbl