A note on proper curvature collineations in Bianchi type VIII and IX space-times

Ghulam Shabbir, Amjad Ali and M. Ramzan1

Abstract

We investigate proper curvature collineations in Bianchi type VIII and IX space-times using the rank of the 6×6 Riemann matrix and direct integration techniques. We found only one case when the above space-times become static and admit proper curvature collineations which form an infinite-dimensional vector space.

References

  1. G. H. Katzin, J. Levine, and W. R. Davis, J. Math. Phys. 10, 617 (1969).
  2. G. S. Hall and J. da. Costa, J. Math. Phys. 32, 2854 (1991).
  3. G. S. Hall, Symmetries and Curvature Structure in General Relativity (World Scientific, 2004).
  4. G. Shabbir, Grav. Cosmol. 9, 139 (2003).
  5. G. Shabbir, Nuovo Cim. B 118, 41 (2003).
  6. G. S. Hall and G. Shabbir, Class. Quantum Grav. 18, 907 (2004).
  7. G. S. Hall, Gen. Rel. Grav. 15, 581 (1983).
  8. A. H. Bokhari, A. Qadir, M. S. Ahmed and M. Asghar, J. Math. Phys. 38, 3639 (1997).
  9. R. A. Tello-Llanos, Gen. Rel. Grav. 20, 765 (1988).
  10. J. Carot and J. da Costa, Gen. Rel. Grav. 23, 1057 (1991).
  11. G. S. Hall, Class. Quantum Grav. 23, 1485 (2006).
  12. G. S. Hall and Lucy MacNay, Class. Quantum Grav. 22, 5191 (2005).
  13. A. H. Bokhari, M. Asghar, M. S. Ahmed, K. Rashid, and G. Shabbir, Nuovo Cim. B 113, 349 (1998).
  14. G. Shabbir, A. H. Bokhari and A. R. Kashif, Nuovo Cim. B 118, 873 (2003).
  15. G. S. Hall and G. Shabbir, Grav. Cosmol. 9, 134 (2003).
  16. G. Shabbir, Nuovo Cim. B 119, 433 (2004).
  17. G. Shabbir, Nuovo Cim. B 121, 319 (2006).
  18. G. Shabbir and Abu Bakar Mehmood, Modern Phys. Lett. A 22, 807 (2007).
  19. G. Shabbir and M. Ramzan, Int. J. Modern Phys. A 23, 749 (2008).
  20. H. Stephani, D. Kramer, M. A. H. MacCallum, C. Hoenselears, and E. Herlt, Exact Solutions of Einstein's Field Equations (Cambridge University Press, 2003).
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