A Berger-Green type inequality for compact Lorentzian manifolds

Gutiérrez, Manuel; Palomo, Francisco; Romero, Alfonso

doi:10.1090/S0002-9947-02-03060-X

A Berger-Green type inequality for compact Lorentzian manifolds

Authors: Manuel Gutiérrez, Francisco J. Palomo and Alfonso Romero
Journal: Trans. Amer. Math. Soc. 354 (2002), 4505-4523
MSC (2000): Primary 53C50, 53C22; Secondary 53C20
DOI: https://doi.org/10.1090/S0002-9947-02-03060-X
Published electronically: July 2, 2002
Erratum: Trans. Amer. Math. Soc. (recently posted)
MathSciNet review: 1926886
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Abstract: We give a Lorentzian metric on the null congruence associated with a timelike conformal vector field. A Liouville type theorem is proved and a boundedness for the volume of the null congruence, analogous to a well-known Berger-Green theorem in the Riemannian case, will be derived by studying conjugate points along null geodesics. As a consequence, several classification results on certain compact Lorentzian manifolds without conjugate points on its null geodesics are obtained. Finally, several properties of null geodesics of a natural Lorentzian metric on each odd-dimensional sphere have been found.

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