East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
권호 표지
DOI QR코드

DOI QR Code

A CHARACTERIZATION THEOREM FOR LIGHTLIKE HYPERSURFACES OF SEMI-RIEMANNIAN MANIFOLDS OF QUASI-CONSTANT CURVATURES

  • Jin, Dae Ho (Department of Mathematics, Dongguk University)
  • Received : 2013.03.28
  • Accepted : 2014.01.13
  • Published : 2014.01.31
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we study lightlike hypersurfaces M of semi-Riemannian manifolds $\bar{M}$ of quasi-constant curvatures. Our main result is a characterization theorem for screen homothetic Einstein lightlike hypersurfaces of a Lorentzian manifold of quasi-constant curvature subject such that its curvature vector field ${\zeta}$ is tangent to M.

Keywords

References

  1. M. C. Chaki and R. K. Maity, On quasi-Einstein manifolds, Publ. Math. Debrecen 57, 2000, 297-306.
  2. B. Y. Chen and K. Yano, Hypersurfaces of a conformally at space, Tensor (N. S.) 26, 1972, 318-322.
  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 Scientic, 2007.
  5. K. L. Duggal and D. H. Jin, A classication of Einstein lightlike hypersurfaces of a Lorentzian space form, J. Geom. Phys., 60, 2010, 1881-1889. https://doi.org/10.1016/j.geomphys.2010.07.005
  6. D. H. Jin, Screen conformal Einstein lightlike hypersurfaces of a Lorentzian space form, Commun. Korean Math. Soc., 25(2), 2010, 225-234. https://doi.org/10.4134/CKMS.2010.25.2.225
  7. D. H. Jin, Lightlike hypersurfaces of a semi-Riemannian manifold of quasi-constant curvature, Commun. Korean Math. Soc., 25(2), 2010, 225-234. https://doi.org/10.4134/CKMS.2010.25.2.225
  8. D. N. Kupeli, Singular Semi-Riemannian Geometry, Mathematics and Its Applications, vol. 366, Kluwer Acad. Publishers, Dordrecht, 1996.