Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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GEOMETRY OF HALF LIGHTLIKE SUBMANIFOLDS OF A SEMI-RIEMANNIAN SPACE FORM WITH A SEMI-SYMMETRIC METRIC CONNECTION

  • Jin, Dae Ho (Department of Mathematics Dongguk University)
  • Received : 2011.08.03
  • Accepted : 2011.11.18
  • Published : 2011.12.30
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Abstract

We study the geometry of half lightlike sbmanifolds M of a semi-Riemannian space form $\tilde{M}(c)$ admitting a semi-symmetric metric connection subject to the conditions: (1) The screen distribution S(TM) is totally umbilical (geodesic) and (2) the co-screen distribution $S(TM^{\bot})$ of M is a conformal Killing one.

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References

  1. B. Y. Chen, Geometry of Submanifolds, Marcel Dekker, New York, 1973.
  2. K. L. Duggal and D. H. Jin, Half-lightlike submanifolds of codimension 2, Math. J. Toyama Univ. 22 (1999), 121-161.
  3. H. A. Hayden, Subspace of a space with torsion, Proc. London Math. Soc. 34 (1932), 27-50. https://doi.org/10.1112/plms/s2-34.1.27
  4. T. Imai, Hypersurfaces of a Riemannian manifold with semi-symmetric metric connection, Tensor, N. S., 23, 1972, 300-306.
  5. D. H. Jin and J. W. Lee, Einstein half lightlike submanifolds of a Lorentzian space form with a semi-symmetric metric connection, to appear Mediterranean J. of Mathematics.
  6. D. N. Kupeli, Singular Semi-Riemannian Geometry, Mathematics and Its Applications, Kluwer Acad. Publishers, Dordrecht, 1996.
  7. Z. Nakao, Submanifolds of a Riemannian manifold with semi-symmetric metric connection, Proc. Amer. Math. Soc. 54 (1976), 261-266. https://doi.org/10.1090/S0002-9939-1976-0445416-9
  8. K. Yano, On semi-symmetric metric connection, Rev. Roumaine Math. Pures Appl. 15 (1970), 1579-1586.