• 제목/요약/키워드: totally umbilical and minimal 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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    • 제57권3호
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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.
    • 대한수학회보
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    • 제50권4호
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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
    • 호남수학학술지
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    • 제44권2호
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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.

CERTAIN RESULTS ON SUBMANIFOLDS OF GENERALIZED SASAKIAN SPACE-FORMS

  • Yadav, Sunil Kumar;Chaubey, Sudhakar K
    • 호남수학학술지
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    • 제42권1호
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    • pp.123-137
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    • 2020
  • The object of the present paper is to study certain geometrical properties of the submanifolds of generalized Sasakian space-forms. We deduce some results related to the invariant and anti-invariant slant submanifolds of the generalized Sasakian spaceforms. Finally, we study the properties of the sectional curvature, totally geodesic and umbilical submanifolds of the generalized Sasakian space-forms. To prove the existence of almost semiinvariant and anti-invariant submanifolds, we provide the non-trivial examples.