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  • Cited by 9
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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Palomo, Francisco J. 2014. A new characterization of the -dimensional Einstein static spacetime. Journal of Geometry and Physics, Vol. 81, p. 112.


    Bavard, Christophe and Mounoud, Pierre 2013. Sur les surfaces lorentziennes compactes sans points conjugués. Geometry & Topology, Vol. 17, Issue. 1, p. 469.


    Duggal, K. L. 2012. A Review on Metric Symmetries Used in Geometry and Physics. ISRN Geometry, Vol. 2012, p. 1.


    Cañadas-Pinedo, María A. Díaz, Ángel Gutiérrez, Manuel and Olea, Benjamín 2010. Curvature and conjugate points in Lorentz symmetric spaces. Annals of Global Analysis and Geometry, Vol. 37, Issue. 1, p. 91.


    Palomo, Francisco J. and Romero, Alfonso 2010. Compact conformally stationary Lorentzian manifolds with no causal conjugate points. Annals of Global Analysis and Geometry, Vol. 38, Issue. 2, p. 135.


    Haesen, Stefan Palomo, Francisco J. and Romero, Alfonso 2009. Null congruence spacetimes constructed from 3-dimensional Robertson–Walker spaces. Differential Geometry and its Applications, Vol. 27, Issue. 2, p. 240.


    HAESEN, STEFAN PALOMO, FRANCISCO J. and ROMERO, ALFONSO 2009. A METHOD TO CONSTRUCT 4-DIMENSIONAL SPACETIMES WITH A SPACELIKE CIRCLE ACTION. International Journal of Geometric Methods in Modern Physics, Vol. 06, Issue. 04, p. 667.


    Palomo, Francisco J. 2007. The fibre bundle of degenerate tangent planes of a Lorentzian manifold and the smoothness of the null sectional curvature. Differential Geometry and its Applications, Vol. 25, Issue. 6, p. 667.


    Palomo, Francisco J. and Romero, Alfonso 2006.


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  • Mathematical Proceedings of the Cambridge Philosophical Society, Volume 137, Issue 2
  • September 2004, pp. 363-375

Lorentzian manifolds with no null conjugate points

  • MANUEL GUTIÉRREZ (a1), FRANCISCO J. PALOMO (a1) (a2) and ALFONSO ROMERO (a3)
  • DOI: http://dx.doi.org/10.1017/S0305004104007674
  • Published online: 01 September 2004
Abstract

An integral inequality for a compact Lorentzian manifold which admits a timelike conformal vector field and has no conjugate points along its null geodesics is given. Moreover, equality holds if and only if the manifold has nonpositive constant sectional curvature. The inequality can be improved if the timelike vector field is assumed to be Killing and, in this case, the equality characterizes (up to a finite covering) flat Lorentzian $n(\geq3)$-dimensional tori. As an indirect application of our technique, it is proved that a Lorentzian $2-$torus with no conjugate points along its timelike geodesics and admitting a timelike Killing vector field must be flat.

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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