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ON HORIZONTAL LIGHTLIKE HYPERSURFACES OF ROBERTSON-WALKER SPACETIMES

Liu, Ximin;Pan, Quanxiang

  • Received : 2014.10.07
  • Published : 2015.04.30

Abstract

In this paper, we investigate horizontal lightlike hypersurfaces of Robertson-Walker spacetimes. Some results involving the unique existence of the screen distribution and the symmetry of the induced Ricci curvature tensor of horizontal lightlike hypersurfaces are presented. We also obtain some properties concerning the symmetry and the parallelism of the second fundamental forms of such lightlike hypersurfaces.

Keywords

lightlike hypersurface;Robertson-Walker spacetime;symmetry;parallelism;induced Ricci curvature tensor

References

  1. L. J. Alias, A. Romero, and M. Sanchez, Uniqueness of complete spacelike hypersurfaces of constant mean curvature in generalized Robertson-Walker spacetimes, Gen. Relativity Gravitation 27 (1995), no. 1, 71-84. https://doi.org/10.1007/BF02105675
  2. C. Atindogbe and K. L. Duggal, Conformal screen on lightlike hypersurfaces, Int. J. Pure Appl. Math. 11 (2004), no. 4, 421-442.
  3. H. Bondi and T. Gold, On the generation of magnestism by fliud motion, Monthly Not. Roy. Astr. Soc. 108 (1948), 252-270. https://doi.org/10.1093/mnras/108.3.252
  4. A. Caminha and H. F. de Lima, Complete vertical graph with constant mean curvature in semi-Riemannian warped products, Bull. Belg. Math. Soc. Simon Stevin 16 (2009), no. 1, 91-105.
  5. K. L. Duggal, A Report on canonical null curves and screen distributions for lightlike geometry, Acta Appl. Math. 95 (2007), no. 2, 135-149. https://doi.org/10.1007/s10440-006-9082-x
  6. K. L. Duggal and A. Bejancu, Lightlike Submainfolds of Semi-Riemannian Mainfolds and Applications, Kluwer Academic Publishers, Dordrecht, 1996.
  7. K. L. Duggal and B. Sahin, Differential Geometry of Lightlike Submanifolds, Birkhauser Veralag AG, Basel, Boston, Berlin, 2010.
  8. S. W. Hawking and G. F. R. Ellis, The Large Scale Structure of Spacetime, Cambridge Univ. Press, Cambridge, 1973.
  9. F. Hoyle, A new model for the expanding universe, Monthly Not. Roy. Astr. Soc. 108 (1948), 372-382. https://doi.org/10.1093/mnras/108.5.372
  10. D. H. Jin, Geometry of lightlike hypersurfaces of an indefinite Sasakian manifold, Indian J. Pure Appl. Math. 41 (2010), no. 4, 569-581. https://doi.org/10.1007/s13226-010-0032-y
  11. T. H. Kang, On lightlike hypersurfaces of a GRW space-time, Bull. Korean Math. Soc. 49 (2012), no. 4, 863-874. https://doi.org/10.4134/BKMS.2012.49.4.863
  12. D. N. Kupeli, Singular Semi-Riemnnian Geometry, Mathematics and Its Applications, Kluwer Academic Publishers, Dordrecht, 1996.
  13. B. O'Neill, Semi-Riemannian Geometry with Application to Relativity, Academic Press, New York, London, 1983.
  14. Y.Wang and X. Liu, On complete spacelike hypersurfaces in a semi-Riemannian warped product, J. Appl. Math. 2013 (2013), Art. ID 757041, 8 pp.

Acknowledgement

Supported by : National Natural Science Foundation of China