• Title/Summary/Keyword: symmetric connection of type (${\ell}$, m)

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LIGHTLIKE HYPERSURFACES OF AN INDEFINITE KAEHLER MANIFOLD WITH A SYMMETRIC METRIC CONNECTION OF TYPE (ℓ, m)

  • Jin, Dae Ho
    • Bulletin of the Korean Mathematical Society
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    • v.53 no.4
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    • pp.1171-1184
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    • 2016
  • We define a new connection on semi-Riemannian manifolds, which is called a symmetric connection of type (${\ell}$, m). Semi-symmetric connection and quarter-symmetric connection are two examples of this connection such that $({\ell},m)=(1,0)$ and $({\ell},m)=(0,1)$ respectively. In this paper, we study lightlike hypersurfaces of an indefinite Kaehler manifold endowed with a symmetric metric connection of type (${\ell}$, m).

LIGHTLIKE HYPERSURFACES OF AN INDEFINITE TRANS-SASAKIAN MANIFOLD WITH AN (ℓ, m)-TYPE CONNECTION

  • Jin, Dae Ho
    • Journal of the Korean Mathematical Society
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    • v.55 no.5
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    • pp.1075-1089
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    • 2018
  • We define a new connection on semi-Riemannian manifolds, which is a non-symmetric and non-metric connection. We say that this connection is an (${\ell}$, m)-type connection. Semi-symmetric non-metric connection and non-metric ${\phi}$-symmetric connection are two important examples of this connection such that (${\ell}$, m) = (1, 0) and (${\ell}$, m) = (0, 1), respectively. In this paper, we study lightlike hypersurfaces of an indefinite trans-Sasakian manifold with an (${\ell}$, m)-type connection.

LIGHTLIKE HYPERSURFACES OF AN INDEFINITE GENERALIZED SASAKIAN SPACE FORM WITH A SYMMETRIC METRIC CONNECTION OF TYPE (ℓ, m)

  • Jin, Dae Ho
    • Communications of the Korean Mathematical Society
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    • v.31 no.3
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    • pp.613-624
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    • 2016
  • We define a new connection on a semi-Riemannian manifold. Its notion contains two well known notions; (1) semi-symmetric connection and (2) quarter-symmetric connection. In this paper, we study the geometry of lightlike hypersurfaces of an indefinite generalized Sasakian space form with a symmetric metric connection of type (${\ell}$, m).

GENERIC LIGHTLIKE SUBMANIFOLDS OF AN INDEFINITE TRANS-SASAKIAN MANIFOLD WITH A NON-SYMMETRIC NON-METRIC CONNECTION OF TYPE (ℓ, m)

  • Lee, Chul Woo;Lee, Jae Won
    • Communications of the Korean Mathematical Society
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    • v.35 no.4
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    • pp.1203-1219
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    • 2020
  • Jin [7] defined a new connection on semi-Riemannian manifolds, which is a non-symmetric and non-metric connection. He said that this connection is an (ℓ, m)-type connection. Jin also studied lightlike hypersurfaces of an indefinite trans-Sasakian manifold with an (ℓ, m)-type connection in [7]. We study further the geometry of this subject. In this paper, we study generic lightlike submanifolds of an indefinite trans-Sasakian manifold endowed with an (ℓ, m)-type connection.