Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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ON LIGHTLIKE HYPERSURFACES OF A GRW SPACE-TIME

  • Received : 2011.04.25
  • Published : 2012.07.31
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Abstract

We provide a study of lightlike hypersurfaces of a generalized Robertson-Walker (GRW) space-time. In particular, we investigate lightlike hypersurfaces with curvature invariance, parallel second fundamental forms, totally umbilical second fundamental forms, null sectional curvatures and null Ricci curvatures, respectively.

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References

  1. A. L. Albujer and S. Haesen, A geometric interpretation of the null sectional curvature, J. Geom. Phys. 60 (2010), no. 3, 471-476. https://doi.org/10.1016/j.geomphys.2009.11.002
  2. C. Atindogbe, J.-P. Ezin, and J. Tossa, Lightlike Einstein hypersurfaces in Lorentzian manifolds with constant curvature, Kodai Math. J. 29 (2006), no. 1, 58-71. https://doi.org/10.2996/kmj/1143122387
  3. J. K. Beem and P. E. Ehrlich, Global Lorentzian Geometry, Marcel Dekker, INC. New York and Basel, 1981.
  4. B.-Y. Chen and J. Van der Veken, Spatial and Lorentzian surfaces in Robertson-Walker space-times, J. Math. Phys. 48 (2007), no. 7, 073509, 12 pp. https://doi.org/10.1063/1.2748616
  5. B.-Y. Chen and S. W. Wei, Differential geometry of submanifolds of warped product manifolds $I{\times}_{f}S^{m-1}$(k), J. Geom. 91 (2009), no. 1-2, 21-42. https://doi.org/10.1007/s00022-008-2035-y
  6. K. L. Duggal and A. Bejancu, Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications, Kluwer Academic Publishers, Dordrecht, 1996.
  7. K. L. Duggal and D. H. Jin, Null curves and Hypersurfaces of Semi-Riemannian Manifolds, World Scientific, 2007.
  8. K. L. Duggal and B. Sahin, Differential geometry of lightlike submanifolds, Birkhauser Verlag AG, 2010.
  9. T. H. Kang, On the geometry of lightlike submanifolds, Kyungpook Math. J. 51 (2011), no. 2, 125-138. https://doi.org/10.5666/KMJ.2011.51.2.125
  10. B. O'Neill, Semi-Riemannian Geometry with Applications to Relativity, Academic Press, New York, 1982.
  11. K. Yano and M. Kon, Structures on Manifold, World Scientific, 1984.

Cited by

  1. Null hypersurfaces in generalized Robertson–Walker spacetimes vol.106, 2016, https://doi.org/10.1016/j.geomphys.2016.04.009
  2. ON LIGHTLIKE SUBMANIFOLDS OF A GRW SPACE-TIME vol.29, pp.2, 2014, https://doi.org/10.4134/CKMS.2014.29.2.295
  3. ON HORIZONTAL LIGHTLIKE HYPERSURFACES OF ROBERTSON-WALKER SPACETIMES vol.30, pp.2, 2015, https://doi.org/10.4134/CKMS.2015.30.2.109
  4. Generalized Robertson-Walker Space-Time Admitting Evolving Null Horizons Related to a Black Hole Event Horizon vol.2016, 2016, https://doi.org/10.1155/2016/9312525
  5. Null Screen Isoparametric Hypersurfaces in Lorentzian Space Forms vol.15, pp.6, 2018, https://doi.org/10.1007/s00009-018-1262-1