• Title/Summary/Keyword: totally umbilical lightlike submanifolds

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Totally Umbilical Slant Lightlike Submanifolds of Indefinite Kaehler Manifolds

  • Sachdeva, Rashmi;Kumar, Rakesh;Bhatia, Satvinder Singh
    • Kyungpook Mathematical Journal
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    • v.57 no.3
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    • pp.503-516
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    • 2017
  • In this paper, we study totally umbilical slant lightlike submanifolds of indefinite Kaehler manifolds. We prove that there do not exist totally umbilical proper slant lightlike submanifolds in indefinite Kaehler manifolds other than totally geodesic proper slant lightlike submanifolds. We also prove that there do not exist totally umbilical proper slant lightlike submanifolds of indefinite Kaehler space forms. Finally, we give a characterization theorem on minimal slant lightlike submanifolds.

GCR-LIGHTLIKE SUBMANIFOLDS OF INDEFINITE NEARLY KAEHLER MANIFOLDS

  • Kumar, Sangeet;Kumar, Rakesh;Nagaich, R.K.
    • Bulletin of the Korean Mathematical Society
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    • v.50 no.4
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    • pp.1173-1192
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    • 2013
  • We introduce CR, SCR and GCR-lightlike submanifolds of indefinite nearly Kaehler manifolds and obtain their existence in indefinite nearly Kaehler manifolds of constant holomorphic sectional curvature $c$ and of constant type ${\alpha}$. We also prove characterization theorems on the existence of totally umbilical and minimal GCR-lightlike submanifolds of indefinite nearly Kaehler manifolds.

GEOMETRIC CHARACTERISTICS OF GENERIC LIGHTLIKE SUBMANIFOLDS

  • Jha, Nand Kishor;Pruthi, Megha;Kumar, Sangeet;Kaur, Jatinder
    • Honam Mathematical Journal
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    • v.44 no.2
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    • pp.179-194
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    • 2022
  • In the present study, we investigate generic lightlike submanifolds of indefinite nearly Kaehler manifolds. After proving the existence of generic lightlike submanifolds in an indefinite generalized complex space form, a non-trivial example of this class of submanifolds is discussed. Then, we find a characterization theorem enabling the induced connection on a generic lightlike submanifold to be a metric connection. We also derive some conditions for the integrability of distributions defined on generic lightlike submanifolds. Further, we discuss the non-existence of mixed geodesic generic lightlike submanifolds in a generalized complex space form. Finally, we investigate totally umbilical generic lightlike submanifolds and minimal generic lightlike submanifolds of an indefinite nearly Kaehler manifold.

SLANT LIGHTLIKE SUBMANIFOLDS OF INDEFINITE NEARLY KAEHLER MANIFOLDS

  • Kumar, Tejinder;Kumar, Sangeet;Kumar, Pankaj
    • Honam Mathematical Journal
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    • v.43 no.2
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    • pp.239-258
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    • 2021
  • In the present paper, we introduce the study of slant lightlike submanifolds of indefinite nearly Kaehler manifolds. After proving some geometric results for the existence of slant lightlike submanifolds of indefinite nearly Kaehler manifolds, we give a non-trivial example of this class of lightlike submanifolds. Then, we derive some conditions for the integrability of the distributions associated with slant lightlike submanifolds of indefinite nearly Kaehler manifolds. Consequently, we study totally umbilical slant lightlike submanifolds of indefinite nearly Kaehler manifolds. Subsequently, we investigate minimal slant lightlike submanifolds of indefinite nearly Kaehler manifolds.

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.

ON LIGHTLIKE SUBMANIFOLDS OF A GRW SPACE-TIME

  • Kang, Tae Ho
    • Communications of the Korean Mathematical Society
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    • v.29 no.2
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    • pp.295-310
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    • 2014
  • This paper provides a study of lightlike submanifolds of a generalized Robertson-Walker (GRW) space-time. In particular, we investigate lightlike submanifolds with curvature invariance, parallel second fundamental forms, totally umbilical second fundamental forms, null sectional curvatures and null Ricci curvatures, respectively.

TRANSVERSAL HALF LIGHTLIKE SUBMANIFOLDS OF AN INDEFINITE SASAKIAN MANIFOLD

  • Jin, Dae-Ho
    • The Pure and Applied Mathematics
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    • v.18 no.1
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    • pp.51-61
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    • 2011
  • In this paper, we study the geometry of transversal half lightlike sub-manifolds of an indefinite Sasakian manifold. The main result is to prove three characterization theorems for such a transversal half lightlike submanifold. In addition to these main theorems, we study the geometry of totally umbilical transversal half lightlike submanifolds of an indefinite Sasakian manifold.

STATICAL HALF LIGHTLIKE SUBMANIFOLDS OF AN INDEFINITE KAEHLER MANIFOLD OF A QUASI-CONSTANT CURVATURE

  • Jin, Dae Ho
    • Communications of the Korean Mathematical Society
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    • v.31 no.2
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    • pp.365-377
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    • 2016
  • In this paper, we study half lightlike submanifolds M of an indefinite Kaehler manifold $\bar{M}$ of quasi-constant curvature such that the characteristic vector field ${\zeta}$ of $\bar{M}$ is tangent to M. First, we provide a new result for such a half lightlike submanifold. Next, we investigate a statical half lightlike submanifold M of $\bar{M}$ subject such that (1) the screen distribution S(TM) is totally umbilical or (2) M is screen conformal.

TRANSVERSAL HALF LIGHTLIKE SUBMANIFOLDS OF AN INDEFINITE KAEHLER MANIFOLD OF A QUASI-CONSTANT CURVATURE

  • Jin, Dae Ho
    • East Asian mathematical journal
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    • v.32 no.1
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    • pp.1-11
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    • 2016
  • We study transversal half lightlike submanifolds of an indefinite Kaehler manifold of a quasi-constant curvature. First, we provide a new result for such a transversal half lightlike submanifold. Next, we investigate a statical half lightlike submanifold M such that (1) the screen distribution S(TM) is totally umbilical, or (2) M is screen homothetic.

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.