• Title, Summary, Keyword: lightlike submanifold

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LIGHTLIKE SUBMANIFOLDS OF AN INDEFINITE QUATERNION KAEHLERIAN MANIFOLD

  • Kang, Tae-Ho
    • East Asian mathematical journal
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    • v.25 no.4
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    • pp.495-504
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    • 2009
  • We introduce three classes of quaternion lightlike submanifolds, screen real lightlike submanifolds and CR lightlike submanifolds of an indefinite quaternion Kaehlerian manifold and study the geometry of leaves of their distributions.

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SLANT LIGHTLIKE SUBMANIFOLDS OF AN INDEFINITE SASAKIAN MANIFOLD

  • Lee, Jae-Won;Jin, Dae-Ho
    • The Pure and Applied Mathematics
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    • v.19 no.2
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    • pp.111-125
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    • 2012
  • In this paper, we introduce the notion of a slant lightlike submanifold of an indefinite Sasakian manifold. We provide a non-trivial example and obtain necessary and sufficient conditions for the existence of a slant lightlike submanifold. Also, we prove some characterization theorems.

Screen Slant Lightlike Submanifolds of Indefinite Kenmotsu Manifolds

  • Gupta, Ram Shankar;Upadhyay, Abhitosh
    • Kyungpook Mathematical Journal
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    • v.50 no.2
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    • pp.267-279
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    • 2010
  • In this paper, we introduce the notion of a screen slant lightlike submanifold of an indefinite Kenmotsu manifold. We provide characterization theorem for existence of screen slant lightlike submanifold with examples. Also, we give an example of a minimal screen slant lightlike submanifold of $R_2^9$ and prove some characterization theorems.

Integrability of Distributions in GCR-lightlike Submanifolds of Indefinite Sasakian Manifolds

  • Jain, Varun;Kumar, Rakesh;Nagaich, Rakesh Kumar
    • Kyungpook Mathematical Journal
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    • v.53 no.2
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    • pp.207-218
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    • 2013
  • In this paper, we study GCR-lightlike submanifolds of indefinite Sasakian manifold. We give some necessary and sufficient conditions on integrability of various distributions of GCR-lightlike submanifold of an indefinite Sasakian manifold. We also find the conditions for each leaf of holomorphic distribution and radical distribution is totally geodesic.

GCR-LIGHTLIKE SUBMANIFOLDS OF A SEMI-RIEMANNIAN PRODUCT MANIFOLD

  • Kumar, Sangeet;Kumar, Rakesh;Nagaich, Rakesh Kumar
    • Bulletin of the Korean Mathematical Society
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    • v.51 no.3
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    • pp.883-899
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    • 2014
  • We introduce GCR-lightlike submanifold of a semi-Riemannian product manifold and give an example. We study geodesic GCR-lightlike submanifolds of a semi-Riemannian product manifold and obtain some necessary and sufficient conditions for a GCR-lightlike submanifold to be a GCR-lightlike product. Finally, we discuss minimal GCR-lightlike submanifolds of a semi-Riemannian product manifold.

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.

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.

NON-EXISTENCE OF LIGHTLIKE SUBMANIFOLDS OF INDEFINITE KAEHLER MANIFOLDS ADMITTING NON-METRIC π-CONNECTIONS

  • Jin, Dae Ho
    • Communications of the Korean Mathematical Society
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    • v.29 no.4
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    • pp.539-547
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    • 2014
  • In this paper, we study two types 1-lightlike submanifolds M, so called lightlike hypersurface and half lightlike submanifold, of an indefinite Kaehler manifold $\bar{M}$ admitting non-metric ${\pi}$-connection. We prove that there exist no such two types 1-lightlike submanifolds of an indefinite Kaehler manifold $\bar{M}$ admitting non-metric ${\pi}$-connections.

NON-EXISTENCE OF LIGHTLIKE SUBMANIFOLDS OF INDEFINITE TRANS-SASAKIAN MANIFOLDS WITH NON-METRIC 𝜃-CONNECTIONS

  • Jin, Dae Ho
    • Communications of the Korean Mathematical Society
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    • v.30 no.1
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    • pp.35-43
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    • 2015
  • We study two types of 1-lightlike submanifolds, so-called lightlike hypersurface and half lightlike submanifold, of an indefinite trans-Sasakian manifold $\bar{M}$ admitting non-metric ${\theta}$-connection. We prove that there exist no such two types of 1-lightlike submanifolds of an indefinite trans-Sasakian manifold $\bar{M}$ admitting non-metric ${\theta}$-connections.