Bayram ŞAHİN

68100

Lightlike Hypersurfaces of Semi-Euclidean Spaces Satisfying Curvature Conditions of Semisymmetry Type

In this paper, we investigate lightlike hypersurfaces which are semi-symmetric, Ricci semi-symmetric, parallel or semi-parallel in a semi-Euclidean space. We obtain that every screen conformal lightlike hypersurface of the Minkowski spacetime is semi-symmetric. For higher dimensions, we show that the semi-symmetry condition of a screen conformal lightlike hypersurface reduces to the semi-symmetry condition of a leaf of its screen distribution. We also obtain that semi-symmetric and Ricci semi-symmetric lightlike hypersurfaces are totally geodesic under certain conditions. Moreover, we show that there exist no non-totally geodesic parallel hypersurfaces in a Lorentzian space.
Anahtar Kelimeler:

Degenerate metric, Screen conformal lightlike hypersurface, Parallel lightlike hypersurface, Semi-symmetric lightlike hypersurface

Lightlike Hypersurfaces of Semi-Euclidean Spaces Satisfying Curvature Conditions of Semisymmetry Type

In this paper, we investigate lightlike hypersurfaces which are semi-symmetric, Ricci semi-symmetric, parallel or semi-parallel in a semi-Euclidean space. We obtain that every screen conformal lightlike hypersurface of the Minkowski spacetime is semi-symmetric. For higher dimensions, we show that the semi-symmetry condition of a screen conformal lightlike hypersurface reduces to the semi-symmetry condition of a leaf of its screen distribution. We also obtain that semi-symmetric and Ricci semi-symmetric lightlike hypersurfaces are totally geodesic under certain conditions. Moreover, we show that there exist no non-totally geodesic parallel hypersurfaces in a Lorentzian space.
Keywords:

Degenerate metric, Screen conformal lightlike hypersurface, Parallel lightlike hypersurface, Semi-symmetric lightlike hypersurface,

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Turkish Journal of Mathematics-Cover
  • ISSN: 1300-0098
  • Yayın Aralığı: 6
  • Yayıncı: TÜBİTAK
Arşiv
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