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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Conformally stationary Lorentzian tori with no conjugate points are flat


Authors: Francisco J. Palomo and Alfonso Romero
Journal: Proc. Amer. Math. Soc. 137 (2009), 2403-2406
MSC (2000): Primary 53C50, 53C22, 53C25
Published electronically: February 24, 2009
MathSciNet review: 2495275
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Abstract: A Lorentzian torus which admits a timelike conformal vector field and with no conjugate points on its timelike and spacelike geodesics is proved to be flat. If only the absence of conjugate points on timelike geodesics is assumed, a counterexample is shown.


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Additional Information

Francisco J. Palomo
Affiliation: Departamento de Matemática Aplicada, Complejo Tecnológico, Universidad de Málaga, 29071-Málaga, Spain
Email: fjpalomo@ctima.uma.es

Alfonso Romero
Affiliation: Departamento de Geometría y Topología, Facultad de Ciencias, Universidad de Granada, 18071-Granada, Spain
Email: aromero@ugr.es

DOI: http://dx.doi.org/10.1090/S0002-9939-09-09847-5
PII: S 0002-9939(09)09847-5
Keywords: Conformally stationary Lorentzian torus, conjugate points, flat Lorentzian torus.
Received by editor(s): June 13, 2008
Published electronically: February 24, 2009
Additional Notes: Both authors were partially supported by the Spanish MEC Grant MTM2007-60731 with FEDER funds and the Junta de Andalucía Regional Grant P06-FQM-01951.
Dedicated: Dedicated to Professor A. M. Naveira on his 68th birthday
Communicated by: Jon G. Wolfson
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.