• Title/Summary/Keyword: almost paracontact Riemannian manifold

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SUBMANIFOLDS OF AN ALMOST r-PARACONTACT RIEMANNIAN MANIFOLD ENDOWED WITH A SEMI-SYMMETRIC METRIC CONNECTION

  • Ahmad, Mobin;Jun, Jae-Bok
    • Honam Mathematical Journal
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    • v.32 no.3
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    • pp.363-374
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    • 2010
  • We define a semi-symmetric metric connection in an almost r-paracontact Riemannian manifold and we consider submanifolds of an almost r-paracontact Riemannian manifold endowed with a semi-symmetric metric connection and obtain Gauss and Codazzi equations, Weingarten equation and curvature tensor for submanifolds of an almost r-paracontact Riemannian manifold endowed with a semi-symmetric metric connection.

SUBMANIFOLDS OF AN ALMOST r-PARACONTACT RIEMANNIAN MANIFOLD ENDOWED WITH A SEMI-SYMMETRIC NON-METRIC CONNECTION

  • Ahmad, Mobin;Jun, Jae-Bok
    • Journal of the Chungcheong Mathematical Society
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    • v.22 no.4
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    • pp.653-665
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    • 2009
  • We define a semi-symmetric non-metric connection in an almost r-paracontact Riemannian manifold and we consider submanifolds of an almost r-paracontact Riemannian manifold endowed with a semi-symmetric non-metric connection and obtain Gauss and Codazzi equations, Weingarten equation and curvature tensor for submanifolds of an almost r-paracontact Riemannian manifold endowed with a semi-symmetric non-metric connection.

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SUBMANIFOLDS OF AN ALMOST r-PARACONTACT RIEMANNIAN MANIFOLD ENDOWED WITH A QUARTER-SYMMETRIC NON-METRIC CONNECTION

  • Ahmad, Mobin;Jun, Jae-Bok;Haseeb, Abdul
    • Journal of the Chungcheong Mathematical Society
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    • v.24 no.1
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    • pp.91-104
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    • 2011
  • We define a quarter-symmetric non-metric connection in an almost r-paracontact Riemannian manifold and we consider the submanifolds of an almost r-paracontact Riemannian manifold endowed with a quarter-symmetric non-metric connection. We also obtain the Gauss, Codazzi and Weingarten equations and the curvature tensor for the submanifolds of an almost r-paracontact Riemannian manifold endowed with a quarter-symmetric non-metric connection.

Hypersurfaces of an almost r-paracontact Riemannian Manifold Endowed with a Quarter Symmetric Non-metric Connection

  • Ahmad, Mobin;Haseeb, Abdul;Ozgur, Cihan
    • Kyungpook Mathematical Journal
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    • v.49 no.3
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    • pp.533-543
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    • 2009
  • We define a quarter symmetric non-metric connection in an almost r-paracontact Riemannian manifold and we consider invariant, non-invariant and anti-invariant hypersurfaces of an almost r-paracontact Riemannian manifold endowed with a quarter symmetric non-metric connection.

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

  • Ahmad, Mobin;Jun, Jae-Bok;Haseeb, Abdul
    • Bulletin of the Korean Mathematical Society
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    • v.46 no.3
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    • pp.477-487
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    • 2009
  • We define a quarter symmetric metric connection in an almost r-paracontact Riemannian manifold and we consider invariant, noninvariant and anti-invariant hypersurfaces of an almost r-paracontact Riemannian manifold endowed with a quarter symmetric metric connection.

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.

ON ALMOST r-PARACONTACT RIEMANNIAN MANIFOLD WITH A CERTAIN CONNECTION

  • Ahmad, Mobin;Haseeb, Abdul;Jun, Jae-Bok;Rahman, Shamsur
    • Communications of the Korean Mathematical Society
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    • v.25 no.2
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    • pp.235-243
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    • 2010
  • In a Riemannian manifold, the existence of a new connection is proved. In particular cases, this connection reduces to several symmetric, semi-symmetric and quarter symmetric connections, even some of them are not introduced so far. So, in this paper, we define a quarter symmetric semi-metric connection in an almost r-paracontact Riemannian manifold and consider invariant, non-invariant and anti-invariant hypersurfaces of an almost r-paracontact Riemannian manifold with that connection.

ANTI-INVARIANT SUBMERSIONS FROM ALMOST PARACONTACT RIEMANNIAN MANIFOLDS

  • Gunduzalp, Yilmaz
    • Honam Mathematical Journal
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    • v.41 no.4
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    • pp.769-780
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    • 2019
  • We introduce anti-invariant Riemannian submersions from almost paracontact Riemannian manifolds onto Riemannian manifolds. We give an example, investigate the geometry of foliations which are arisen from the definition of a Riemannian submersion and check the harmonicity of such submersions.