• Title/Summary/Keyword: semi-invariant

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ON SEMI-INVARIANT SUBMANIFOLDS OF A NEARLY KENMOTSU MANIFOLD WITH A SEMI-SYMMETRIC NON-METRIC CONNECTION

  • Ahmad, Mobin;Jun, Jae-Bok
    • Journal of the Chungcheong Mathematical Society
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    • v.23 no.2
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    • pp.257-266
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    • 2010
  • We define a semi-symmetric non-metric connection in a nearly Kenmotsu manifold and we study semi-invariant submanifolds of a nearly Kenmotsu manifold endowed with a semi-symmetric non-metric connection. Moreover, we discuss the integrability of distributions on semi-invariant submanifolds of a nearly Kenmotsu manifold with a semi-symmetric non-metric connection.

WARPED PRODUCT SKEW SEMI-INVARIANT SUBMANIFOLDS OF LOCALLY GOLDEN RIEMANNIAN MANIFOLDS

  • Ahmad, Mobin;Qayyoom, Mohammad Aamir
    • Honam Mathematical Journal
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    • v.44 no.1
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    • pp.1-16
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    • 2022
  • In this paper, we define and study warped product skew semi-invariant submanifolds of a locally golden Riemannian manifold. We investigate a necessary and sufficient condition for a skew semi-invariant submanifold of a locally golden Riemannian manifold to be a locally warped product. An equality between warping function and the squared normed second fundamental form of such submanifolds is established. We also construct an example of warped product skew semi-invariant submanifolds.

ON SEMI-INVARIANT SUBMANIFOLDS OF LORENTZIAN ALMOST PARACONTACT MANIFOLDS

  • Tripathi, Mukut-Mani
    • The Pure and Applied Mathematics
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    • v.8 no.1
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    • pp.1-8
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    • 2001
  • Semi-invariant submanifolds of Lorentzian almost paracontact mani-folds are studied. Integrability of certain distributions on the submanifold are in vestigated. It has been proved that a LP-Sasakian manifold does not admit a proper semi-invariant submanifold.

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ON SOME PROPERTIES OF SEMI-INVARIANT SUBMANIFOLDS OF A NEARLY TRANS-SASAKIAN MANIFOLD ADMITTING A QUARTER-SYMMETRIC NON-METRIC CONNECTION

  • Ahmad, Mobin;Jun, Jae-Bok;Siddiqi, Mohd Danish
    • Journal of the Chungcheong Mathematical Society
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    • v.25 no.1
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    • pp.73-90
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    • 2012
  • We define a quarter-symmetric non-metric connection in a nearly trans-Sasakian manifold and we consider semi-invariant submanifolds of a nearly trans-Sasakian manifold endowed with a quarter-symmetric non-metric connection. Moreover, we also obtain integrability conditions of the distributions on semi-invariant submanifolds.

ON SEMI-INVARIANT SUBMANIFOLDS OF A NEARLY KENMOTSU MANIFOLD WITH A QUARTER SYMMETRIC NON-METRIC CONNECTION

  • Ahmad, Mobin;Jun, Jae-Bok
    • The Pure and Applied Mathematics
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    • v.18 no.1
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    • pp.1-11
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    • 2011
  • We define a quarter symmetric non-metric connection in a nearly Ken-motsu manifold and we study semi-invariant submanifolds of a nearly Kenmotsu manifold endowed with a quarter symmetric non-metric connection. Moreover, we discuss the integrability of the distributions on semi-invariant submanifolds of a nearly Kenmotsu manifold with a quarter symmetric non-metric connection.

LORENTZIAN ALMOST PARACONTACT MANIFOLDS AND THEIR SUBMANIFOLDS

  • Tripathi, Mukut-Mani;De, Uday-Chand
    • The Pure and Applied Mathematics
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    • v.8 no.2
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    • pp.101-125
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    • 2001
  • This is a survey article on almost Lorentzian paracontact manifolds. The study of Lorentsian almost paracontact manifolds was initiated by Matsumoto [On Lorentzian paracontact manifolds, Bull. Yamagata Univ. Nat. Sci. 12 (1989), 151-l56]. Later on several authors studied Lorentzian almost paracontact manifolds and their different classes, viz. LP-Sasakian and LSP-Sasakian manifolds. Different types of submanifolds, for example invariant, semi-invariant and almost semi-invariant, of Lorentzian almost paracontact manifold have been studied. Here, we present a brief survey of results on Lorentzian almost paracontact manifolds with their different classes and their different kind of submanifolds.

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INVARIANT SUBMANIFOLDS OF (LCS)n-MANIFOLDS ADMITTING CERTAIN CONDITIONS

  • Eyasmin, Sabina;Baishya, Kanak Kanti
    • Honam Mathematical Journal
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    • v.42 no.4
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    • pp.829-841
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    • 2020
  • The object of the present paper is to study the invariant submanifolds of (LCS)n-manifolds. We study generalized quasi-conformally semi-parallel and 2-semiparallel invariant submanifolds of (LCS)n-manifolds and showed their existence by a non-trivial example. Among other it is shown that an invariant submanifold of a (LCS)n-manifold is totally geodesic if the second fundamental form is any one of (i) symmetric, (ii) recurrent, (iii) pseudo symmetric, (iv) almost pseudo symmetric and (v) weakly pseudo symmetric.

SEMI-INVARIANT SUBMANIFOLDS OF CODIMENSION 3 SATISFYING 𝔏ξ∇ = 0 IN A NONFLAT COMPLEX SPACE FORM

  • AHN, SEONG-SOO;LEE, SEONG-BAEK;LEE, AN-AYE
    • Honam Mathematical Journal
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    • v.23 no.1
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    • pp.133-143
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    • 2001
  • In this paper, we characterize some semi-invariant submanifolds of codimension 3 with almost contact metric structure (${\phi}$, ${\xi}$, g) satisfying 𝔏ξ∇ = 0 in a nonflat complex space form, where ${\nabla}$ denotes the Riemannian connection induced on the submanifold, and 𝔏ξ is the operator of the Lie derivative with respect to the structure vector field ${\xi}$.

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SEMI-INVARIANT SUBMANIFOLDS OF CODIMENSION 3 OF A COMPLEX PROJECTIVE SPACE IN TERMS OF THE JACOBI OPERATOR

  • HER, JONG-IM;KI, U-HANG;LEE, SEONG-BAEK
    • Bulletin of the Korean Mathematical Society
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    • v.42 no.1
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    • pp.93-119
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    • 2005
  • In this paper, we characterize some semi-invariant sub-manifolds of codimension 3 with almost contact metric structure ($\phi$, $\xi$, g) in a complex projective space $CP^{n+1}$ in terms of the structure tensor $\phi$, the Ricci tensor S and the Jacobi operator $R_\xi$ with respect to the structure vector $\xi$.

HYPERSURFACES OF ALMOST γ-PARACONTACT RIEMANNIAN MANIFOLD ENDOWED WITH SEMI-SYMMETRIC METRIC CONNECTION

  • Jun, Jae-Bok;Ahmad, Mobin
    • Bulletin of the Korean Mathematical Society
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    • v.46 no.5
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    • pp.895-903
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    • 2009
  • We define a semi-symmetric metric connection in an almost $\gamma$-paracontact Riemannian manifold and we consider invariant, non-invariant and anti-invariant hypersurfaces of an almost $\gamma$-paracontact Riemannian manifold endowed with a semi-symmetric metric connection.