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Completeness of compact Lorentz manifolds admitting a timelike conformal Killing vector field


Authors: Alfonso Romero and Miguel Sánchez
Journal: Proc. Amer. Math. Soc. 123 (1995), 2831-2833
MSC: Primary 53C50; Secondary 57R20, 57S25
MathSciNet review: 1257122
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Abstract: It is proved that every compact Lorentz manifold admitting a timelike conformal Killing vector field is geodesically complete. So, a recent result by Kamishima in J. Differential Geometry [37 (1993), 569-601] is widely extended.


References [Enhancements On Off] (What's this?)

  • [1] Yves Carrière, Autour de la conjecture de L. Markus sur les variétés affines, Invent. Math. 95 (1989), no. 3, 615–628 (French, with English summary). MR 979369, 10.1007/BF01393894
  • [2] Yoshinobu Kamishima, Completeness of Lorentz manifolds of constant curvature admitting Killing vector fields, J. Differential Geom. 37 (1993), no. 3, 569–601. MR 1217161
  • [3] A. Romero and M. Sánchez, Incomplete Lorentzian tori with a Killing vector field, preprint, Univ. Granada, 1993.
  • [4] Joseph A. Wolf, Spaces of constant curvature, McGraw-Hill Book Co., New York-London-Sydney, 1967. MR 0217740

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1995-1257122-3
Keywords: Compact Lorentz manifolds, geodesic completeness, conformal Killing vector fields, timelike vector fields
Article copyright: © Copyright 1995 American Mathematical Society