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Timelike isometries and killing fields

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References

  1. Avez, A., ‘Essais de géométrie Riemannienne hyperbolique globale — Applications á la relativité générale’, Ann. Inst. Fourier 13, 2(1963), 105–190.

    Article  MathSciNet  MATH  Google Scholar 

  2. Beem, J. K. and Ehrlich, P. E., Global Lorentzian Geometry, Marcel Dekker Monographs in Pure and Applied Mathematics, Vol. 67, Marcel Dekker, New York, 1981.

    Google Scholar 

  3. Bishop, R. L. and O'Neill, B., ‘Manifolds of Negative Curvature’, Trans. Amer. Math. Soc. 145 (1969), 1–49.

    Article  MathSciNet  MATH  Google Scholar 

  4. Cheeger, J. and Ebin, D., Comparison Theorems in Riemannian Geometry, North-Holland Mathematical Library, Vol. 9, 1975.

  5. Ehrlich, P. E., ‘The Displacement Function of a Timelike Isometry’, Tensor (N.S.) 38 (1982), 29–36.

    MathSciNet  MATH  Google Scholar 

  6. Flaherty, F., ‘Lorentzian Manifolds of Nonpositive Curvature’, Proc. Symp. Pure Math. 27 (Pt 2), Amer. Math. Soc., 1975, 393–399.

    MATH  Google Scholar 

  7. Flaherty, F., ‘Lorentzian Manifolds of Nonpositive Curvature II, Proc. Amer. Math. Soc. 48 (1975), 199–202.

    Article  MathSciNet  MATH  Google Scholar 

  8. Hawking, S. and Ellis, G., The Large Scale Structure of Space-time, Camb. Univ. Press Monographs on Math. Phys., Cambridge, 1973.

    Book  MATH  Google Scholar 

  9. Kobayashi, S. and Avérous, G., ‘On Automorphisms of Spaces of Nonpositive Curvature with Finite Volume’ in Differential Geometry and Relativity (eds Cahen and Flato ), D. Reidel, Dordrecht, Holland, 1976, pp. 19–26.

    Google Scholar 

  10. Kobayashi, S. and Nomizu, K., Foundations of Differential Geometry, Tracts in Mathematics, 15, Vol. I (1963) and Vol. II (1969), John Wiley, New York.

    MATH  Google Scholar 

  11. O'Neill, B., Semi-Riemannian Geometry, Academic Press Series in Pure and Applied Math., 103, Academic Press, New York, 1983.

    Google Scholar 

  12. Ozols, V., ‘Critical Points of the Displacement Function of an Isometry’, J. Diff. Geom. 3 (1969), 411–432.

    MathSciNet  MATH  Google Scholar 

  13. Ozols, V., ‘Critical Points of the Length of a Killing Field’, J. Diff. Geom. 7 (1972), 143–148.

    MathSciNet  MATH  Google Scholar 

  14. Ozols, V., ‘Critical Sets of Isometries’, Proc. Symp. Pure Math. 27, Amer. Math. Soc., 1975, pp. 375–378.

    Article  MathSciNet  MATH  Google Scholar 

  15. Smith, J., ‘Fundamental Groups on a Lorentz Manifold’, Amer. J. Math. 82 (1960), 873–890.

    Article  MathSciNet  MATH  Google Scholar 

  16. Yau, S. T., ‘Non-existence of Continuous Convex Functions on Certain Riemannian Manifolds, Math. Ann. 207 (1974), 269–270.

    Article  MathSciNet  MATH  Google Scholar 

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Supported in part by the National Science Foundation under grant number DMS-8601342.

Supported in part by the Danish Natural Science Research Council.

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Beem, J.K., Ehrlich, P.E. & Markvorsen, S. Timelike isometries and killing fields. Geom Dedicata 26, 247–258 (1988). https://doi.org/10.1007/BF00183017

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