• Title/Summary/Keyword: semi-symmetric metric connections

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CURVATURES OF SEMI-SYMMETRIC METRIC CONNECTIONS ON STATISTICAL MANIFOLDS

  • Balgeshir, Mohammad Bagher Kazemi;Salahvarzi, Shiva
    • Communications of the Korean Mathematical Society
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    • v.36 no.1
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    • pp.149-164
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    • 2021
  • By using a statistical connection, we define a semi-symmetric metric connection on statistical manifolds and study the geometry of these manifolds and their submanifolds. We show the symmetry properties of the curvature tensor with respect to the semi-symmetric metric connections. Also, we prove the induced connection on a submanifold with respect to a semi-symmetric metric connection is a semi-symmetric metric connection and the second fundamental form coincides with the second fundamental form of the Levi-Civita connection. Furthermore, we obtain the Gauss, Codazzi and Ricci equations with respect to the new connection. Finally, we construct non-trivial examples of statistical manifolds admitting a semi-symmetric metric connection.

SOME NOTES ON LP-SASAKIAN MANIFOLDS WITH GENERALIZED SYMMETRIC METRIC CONNECTION

  • Bahadir, Oguzhan;Chaubey, Sudhakar K.
    • Honam Mathematical Journal
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    • v.42 no.3
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    • pp.461-476
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    • 2020
  • The present study initially identify the generalized symmetric connections of type (α, β), which can be regarded as more generalized forms of quarter and semi-symmetric connections. The quarter and semi-symmetric connections are obtained respectively when (α, β) = (1, 0) and (α, β) = (0, 1). Taking that into account, a new generalized symmetric metric connection is attained on Lorentzian para-Sasakian manifolds. In compliance with this connection, some results are obtained through calculation of tensors belonging to Lorentzian para-Sasakian manifold involving curvature tensor, Ricci tensor and Ricci semi-symmetric manifolds. Finally, we consider CR-submanifolds admitting a generalized symmetric metric connection and prove many interesting results.

NON-TANGENTIAL HALF LIGHTLIKE SUBMANIFOLDS OF SEMI-RIEMANNIAN MANIFOLDS WITH SEMI-SYMMETRIC NON-METRIC CONNECTIONS

  • Jin, Dae Ho
    • Journal of the Korean Mathematical Society
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    • v.51 no.2
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    • pp.311-323
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    • 2014
  • In this paper, we construct two types of non-tangential half lightlike submanifolds of a semi-Riemannian manifold admitting a semi-symmetric non-metric connection. Our main result is to prove several characterization theorems for each types of such half lightlike submanifolds equipped with totally geodesic screen distributions.

RESULTS CONCERNING SEMI-SYMMETRIC METRIC F-CONNECTIONS ON THE HSU-B MANIFOLDS

  • Uday Chand De;Aydin Gezer;Cagri Karaman
    • Communications of the Korean Mathematical Society
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    • v.38 no.3
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    • pp.837-846
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    • 2023
  • In this paper, we firstly construct a Hsu-B manifold and give some basic results related to it. Then, we address a semi-symmetric metric F-connection on the Hsu-B manifold and obtain the curvature tensor fields of such connection, and study properties of its curvature tensor and torsion tensor fields.

η-Ricci Solitons in δ-Lorentzian Trans Sasakian Manifolds with a Semi-symmetric Metric Connection

  • Siddiqi, Mohd Danish
    • Kyungpook Mathematical Journal
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    • v.59 no.3
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    • pp.537-562
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    • 2019
  • The aim of the present paper is to study the ${\delta}$-Lorentzian trans-Sasakian manifold endowed with semi-symmetric metric connections admitting ${\eta}$-Ricci Solitons and Ricci Solitons. We find expressions for the curvature tensor, the Ricci curvature tensor and the scalar curvature tensor of ${\delta}$-Lorentzian trans-Sasakian manifolds with a semisymmetric-metric connection. Also, we discuses some results on quasi-projectively flat and ${\phi}$-projectively flat manifolds endowed with a semi-symmetric-metric connection. It is shown that the manifold satisfying ${\bar{R}}.{\bar{S}}=0$, ${\bar{P}}.{\bar{S}}=0$ is an ${\eta}$-Einstein manifold. Moreover, we obtain the conditions for the ${\delta}$-Lorentzian trans-Sasakian manifolds with a semisymmetric-metric connection to be conformally flat and ${\xi}$-conformally flat.

OPTIMAL INEQUALITIES FOR THE CASORATI CURVATURES OF SUBMANIFOLDS OF GENERALIZED SPACE FORMS ENDOWED WITH SEMI-SYMMETRIC METRIC CONNECTIONS

  • LEE, CHUL WOO;LEE, JAE WON;VILCU, GABRIEL-EDUARD;YOON, DAE WON
    • Bulletin of the Korean Mathematical Society
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    • v.52 no.5
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    • pp.1631-1647
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    • 2015
  • In this paper, we prove two optimal inequalities involving the intrinsic scalar curvature and extrinsic Casorati curvature of submanifolds of generalized space forms endowed with a semi-symmetric metric connection. Moreover, we also characterize those submanifolds for which the equality cases hold.

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.

GEOMETRIC INEQUALITIES FOR WARPED PRODUCTS SUBMANIFOLDS IN GENERALIZED COMPLEX SPACE FORMS

  • Mohd Aquib;Mohd Aslam;Michel Nguiffo Boyom;Mohammad Hasan Shahid
    • Communications of the Korean Mathematical Society
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    • v.38 no.1
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    • pp.179-193
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    • 2023
  • In this article, we derived Chen's inequality for warped product bi-slant submanifolds in generalized complex space forms using semisymmetric metric connections and discuss the equality case of the inequality. Further, we discuss non-existence of such minimal immersion. We also provide various applications of the obtained inequalities.