• Title/Summary/Keyword: indefinite Sasakian manifold

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INDEFINITE TRANS-SASAKIAN MANIFOLD WITH A TRANSVERSAL HALF LIGHTLIKE SUBMANIFOLD

  • Jin, Dae Ho
    • East Asian mathematical journal
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    • v.33 no.5
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    • pp.533-542
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    • 2017
  • We study the geometry of indefinite trans-Sasakian manifold ${\bar{M}}$ admitting a half lightlike submanifold M such that the structure vector field of ${\bar{M}}$ belongs to the transversal vector bundle of M. We prove several classification theorems of such an indefinite trans-Sasakian manifold.

INDEFINITE TRANS-SASAKIAN MANIFOLD ADMITTING AN ASCREEN HALF LIGHTLIKE SUBMANIFOLD

  • Jin, Dae Ho
    • Communications of the Korean Mathematical Society
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    • v.29 no.3
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    • pp.451-461
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    • 2014
  • We study the geometry of indefinite trans-Sasakian manifold $\bar{M}$, of type (${\alpha},{\beta}$), admitting a half lightlike submanifold M such that the structure vector field of $\bar{M}$ does not belong to the screen and coscreen distributions of M. The purpose of this paper is to prove several classification theorems of such an indefinite trans-Sasakian manifold.

TRANSVERSAL LIGHTLIKE SUBMERSIONS FROM INDEFINITE SASAKIAN MANIFOLDS ONTO LIGHTLIKE MANIFOLDS

  • Shiv Sharma Shukla;Vipul Singh
    • Communications of the Korean Mathematical Society
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    • v.38 no.4
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    • pp.1191-1213
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    • 2023
  • In this paper, we introduce and study two new classes of lightlike submersions, called radical transversal and transversal lightlike submersions between an indefinite Sasakian manifold and a lightlike manifold. We give examples and investigate the geometry of distributions involved in the definitions of these lightlike submersions. We also study radical transversal and transversal lightlike submersions from an indefinite Sasakian manifold onto a lightlike manifold with totally contact umbilical fibers.

SPECIAL HALF LIGHTLIKE SUBMANIFOLDS OF AN INDEFINITE SASAKIAN MANIFOLD

  • Jin, Dae Ho
    • Communications of the Korean Mathematical Society
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    • v.29 no.1
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    • pp.109-121
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    • 2014
  • In this paper, we study the geometry of half lightlike submanifolds of an indefinite Sasakian manifold. There are several different types of half lightlike submanifolds of an indefinite Sasakian manifold according to the form of its structure vector field. We study two types of them here: tangential and ascreen half lightlike submanifolds.

HALF LIGHTLIKE SUBMANIFOLDS OF AN INDEFINITE SASAKIAN MANIFOLD

  • Jin, Dae-Ho
    • The Pure and Applied Mathematics
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    • v.18 no.2
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    • pp.173-183
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    • 2011
  • We study half lightlike submanifolds of an indefinite Sasakian manifold. The aim of this paper is to prove the following result: If a locally symmetric half lightlike submanifold of an indefinite Sasakian manifold is totally umbilical, then it is of constant positive curvature 1. In addition to this result, we prove three characterization theorems for such a half lightlike submanifold.

HALF LIGHTLIKE SUBMANIFOLDS OF AN INDEFINITE TRANS-SASAKIAN MANIFOLD WITH A QUARTER-SYMMETRIC METRIC CONNECTION

  • Jin, Dae Ho
    • East Asian mathematical journal
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    • v.33 no.5
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    • pp.543-557
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    • 2017
  • Jin [10] studied lightlike hypersurfaces of an indefinite trans-Sasakian manifold with a quarter-symmetric metric connection. We study further the geometry of this subject. The object of this paper is to study the geometry of half lightlike submanifolds of an indefinite trans-Sasakian manifold with a quarter-symmetric metric connection.

HALF LIGHTLIKE SUBMANIFOLDS OF AN INDEFINITE TRANS-SASAKIAN MANIFOLD OF QUASI-CONSTANT CURVATURE

  • JIN, DAE HO
    • The Pure and Applied Mathematics
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    • v.22 no.2
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    • pp.113-125
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    • 2015
  • We study half lightlike submanifolds M of an indefinite trans-Sasakian manifold of quasi-constant curvature subject to the condition that the 1-form θ and the vector field ζ, defined by (1.1), are identical with the 1-form θ and the vector field ζ of the indefinite trans-Sasakian structure { J, θ, ζ } of .

HALF LIGHTLIKE SUBMANIFOLDS OF AN INDEFINITE TRANS-SASAKIAN MANIFOLD

  • Jin, Dae Ho
    • Bulletin of the Korean Mathematical Society
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    • v.51 no.4
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    • pp.979-994
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    • 2014
  • We study half lightlike submanifold M of an indefinite trans-Sasakian manifold such that its structure vector field is tangent to M. First we study the general theory for such half lightlike submanifolds. Next we prove some characterization theorems for half lightlike submanifolds of an indefinite generalized Sasakian space form.