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Conformally stationary Lorentzian tori with no conjugate points are flat
Author(s):
Francisco
J.
Palomo;
Alfonso
Romero
Journal:
Proc. Amer. Math. Soc.
137
(2009),
2403-2406.
MSC (2000):
Primary 53C50, 53C22, 53C25
Posted:
February 24, 2009
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Additional information
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.
References:
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- 2.
- D. Burago and S. Ivanov, Riemannian tori without conjugate points are flat, Geom. Funct. Anal., 4 (1994), 259-269. MR 1274115 (95h:53049)
- 3.
- J.L. Flores and M. Sánchez, Geodesic connectedness and conjugate points in GRW space-times, J. Geom. Phys., 36 (2000), 285-314. MR 1793013 (2001g:58024)
- 4.
- M. Gutiérrez, F.J. Palomo and A. Romero, A Berger-Green type inequality for compact Lorentzian manifolds, Trans. Amer. Math. Soc., 354 (2002), 4505-4523. (Erratum Trans. Amer. Math. Soc., 355 (2003), 5119-5120). MR 1926886 (2003h:53098), MR 1997597 (2004g:53076)
- 5.
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- 7.
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- 8.
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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:
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
Posted:
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
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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