Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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LIGHTLIKE HYPERSURFACES OF AN INDEFINITE KAEHLER MANIFOLD WITH A QUARTER-SYMMETRIC METRIC CONNECTION

  • Jin, Dae Ho (Department of Mathematics Dongguk University)
  • Received : 2013.12.16
  • Published : 2015.01.31
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Abstract

In this paper, we study lightlike hypersurfaces of an indefinite Kaehler manifold with a quarter-symmetric metric connection. We prove several classification theorems for such a lightlike hypersurface.

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References

  1. C. Atindogbe and K. L. Duggal, Conformal screen on lightlike hypersurfaces, Int. J. Pure Appl. Math. 11 (2004), no. 4, 421-442.
  2. G. de Rham, Sur la reductibilite d'un espace de Riemannian, Comment. Math. Helv. 26 (1952), 328-344. https://doi.org/10.1007/BF02564308
  3. K. L. Duggal and A. Bejancu, Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications, Kluwer Acad. Publishers, Dordrecht, 1996.
  4. K. L. Duggal and D. H. Jin, Null curves and Hypersurfaces of Semi-Riemannian Manifolds, World Scientific, 2007.
  5. K. L. Duggal and D. H. Jin, A classification of Einstein lightlike hypersurfaces of a Lorentzian space form, J. Geom. Phys. 60 (2010), no. 12, 1881-1889. https://doi.org/10.1016/j.geomphys.2010.07.005
  6. K. L. Duggal and B. Sahin, Differential Geometry of Lightlike Submanifolds, Frontiers in Mathematics, Birkhauser, 2010.
  7. S. Golab, On semi-symmetric and quarter-symmetric connections, Tensor (N.S.) 29 (1975), 249-254.
  8. D. Kamilya and U. C. De, Some properties of a Ricci quarter-symmetric metric connection in a Riemannian manifold, Indian J. Pure Appl. Math. 26 (1995), no. 1, 29-34.
  9. R. S. Mishra and S. N. Pandey, On quarter-symmetric F-connections, Tensor (N.S.) 34 (1980), no. 1, 1-7.
  10. J. Nikic and N. Pusic, A remakable class of natural metric quarter-symmetric connection on a hyperbolic Kaehler space, Conference "Applied Differential Geometry: General Relativity"-Workshop "Global Analysis, Differential Geometry, Lie Algebras", 96-101, BSG Proc., 11, Geom. Balkan Press, Bucharest, 2004.
  11. B. O'Neill, Semi-Riemannian Geometry with Applications to Relativity, Academic Press, 1983.
  12. N. Pusic, On quarter-symmetric metric connections on a hyperbolic Kaehler space, Publ. de l' Inst. Math. 73(87) (2003), 73-80. https://doi.org/10.2298/PIM0373073P
  13. S. C. Rastogi, On quarter-symmetric metric connections, C. R. Acad Bulgare Sci. 31 (1978), no. 7, 811-814.
  14. S. C. Rastogi, On quarter-symmetric metric connections, Tensor (N.S.) 44 (1987), no. 2, 133-141.
  15. K. Yano and T. Imai, Quarter-symmwtric metric connection and their curvature tensors, Tensor (N.S.) 38 (1982), 13-18.