대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제27권4호
  • /
  • Pages.763-770
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  • 2012
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  • 1225-1763(pISSN)
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  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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LIGHTLIKE HYPERSURFACES OF A SEMI-RIEMANNIAN MANIFOLD OF QUASI-CONSTANT CURVATURE

  • Jin, Dae-Ho (Department of Mathematics Dongguk University)
  • 투고 : 2011.07.05
  • 발행 : 2012.10.31
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초록

In this paper, we study the geometry lightlike hypersurfaces (M, $g$, S(TM)) of a semi-Riemannian manifold ($\tilde{M}$, $\tilde{g}$) of quasi-constant curvature subject to the conditions: (1) The curvature vector field of $\tilde{M}$ is tangent to M, and (2) the screen distribution S(TM) is either totally geodesic in M or totally umbilical in $\tilde{M}$.

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참고문헌

  1. M. C. Chaki and R. K. Maity, On quasi-Einstein manifolds, Publ. Math. Debrecen 57 (2000), no. 3-4, 297-306.
  2. B. Y. Chen and K. Yano, Hypersurfaces of a conformally flat space, Tensor (N. S.) 26 (1972), 318-322.
  3. K. L. Duggal, On scalar curvature in lightlike geometry, J. Geom. Phys. 57 (2007), no. 2, 473-481. https://doi.org/10.1016/j.geomphys.2006.04.001
  4. K. L. Duggal and A. Bejancu, Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications, Kluwer Acad. Publishers, Dordrecht, 1996.
  5. K. L. Duggal and D. H. Jin, Null curves and Hypersurfaces of Semi-Riemannian Manifolds, World Scientific, 2007.
  6. 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

피인용 문헌

  1. A SEMI-RIEMANNIAN MANIFOLD OF QUASI-CONSTANT CURVATURE ADMITS SOME HALF LIGHTLIKE SUBMANIFOLDS vol.50, pp.3, 2013, https://doi.org/10.4134/BKMS.2013.50.3.1041
  2. LIGHTLIKE HYPERSURFACES OF INDEFINITE KAEHLER MANIFOLDS OF QUASI-CONSTANT CURVATURES vol.30, pp.5, 2014, https://doi.org/10.7858/eamj.2014.039