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Ascreen lightlike hypersurfaces of a semi-Riemannian space form with a semi-symmetric non-metric connection

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We study lightlike hypersurfaces of a semi-Riemannian space form fM(c) admitting a semi-symmetric non-metric connection. First, we construct a type of lightlike hypersurfaces according to the form of the structure vector field of fM(c), which is called a ascreen lightlike hypersurface. Next, we prove a characterization theorem for such an ascreen lightlike hypersurface endow with a totally geodesic screen distribution.

Abstract

We study lightlike hypersurfaces of a semi-Riemannian space form fM(c) admitting a semi-symmetric non-metric connection. First, we construct a type of lightlike hypersurfaces according to the form of the structure vector field of fM(c), which is called a ascreen lightlike hypersurface. Next, we prove a characterization theorem for such an ascreen lightlike hypersurface endow with a totally geodesic screen distribution.

참고문헌 (13)

  1. N. S. Agashe, "A semi-symmetric non-metric connection on a Riemannian manifold", Indian J. Pure Appl. Math, 23(6), pp.399~409 (1992)
  2. G. de Rham, "Sur la reductibilit´e d’un espace de Riemannian", Comment. Math. Helv, 26, pp.328~344 (1952)
  3. K. L. Duggal, "Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications" (1996), Kluwer Acad. Publishers
  4. K. L. Duggal, "Null curves and Hypersurfaces of Semi-Riemannian Manifolds" (2007), World Scientific
  5. K. L. Duggal, "Differential Geometry of Lightlike Submanifolds, Frontiers in Mathematics", Birkhauser (2010)
  6. Dae Ho Jin, "TRANSVERSAL HALF LIGHTLIKE SUBMANIFOLDS OF AN INDEFINITE SASAKIAN MANIFOLD", 순수 및 응용수학, 18(1), pp.51~61 (2011), 한국수학교육학회
  7. D. H. Jin, "Special half lightlike submanifolds", J. Funct. Spaces Appl, 2012 (2012)
  8. Dae Ho Jin, "ASCREEN LIGHTLIKE HYPERSURFACES OF AN INDEFINITE SASAKIAN MANIFOLD", 순수 및 응용수학, 20(1), pp.25~35 (2013), 한국수학교육학회
  9. D. H. Jin, "Geometry of lightlike hypersurfaces of a semi-Riemannian space form with a semi-symmetric non-metric connection", submittied in Indian J. Pure Appl. Math, ~
  10. 진대호, "Einstein lightlike hypersurfaces of a Lorentz space form with a semi-symmetric non-metric connection", 대한수학회보, 50(4), pp.1367~1376 (2013), 대한수학회
  11. D. H. Jin, "Two characterization theorems for lightlike geometry", submitted in Honam Math. J, ~
  12. D. H. Jin, "A classification of screen quasi-conformal Einstein lightlike hypersurfaces of a semi-Riemannian space form with a semi-symmetric non-metric connection", submitted in J. Fun. Sp. Math, ~
  13. E. Yasar, "Lightlike hypersurfaces in semi-Riemannian manifold with semi-symmetric non-metric connection", Math. Scand, 102(2), pp.253~264 (2008)

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