• Title/Summary/Keyword: Ricci-semisymmetric manifolds

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SOME NOTES ON NEARLY COSYMPLECTIC MANIFOLDS

  • Yildirim, Mustafa;Beyendi, Selahattin
    • Honam Mathematical Journal
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    • v.43 no.3
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    • pp.539-545
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    • 2021
  • In this paper, we study some symmetric and recurrent conditions of nearly cosymplectic manifolds. We prove that Ricci-semisymmetric and Ricci-recurrent nearly cosymplectic manifolds are Einstein and conformal flat nearly cosymplectic manifold is locally isometric to Riemannian product ℝ × N, where N is a nearly Kähler manifold.

Some Geometric Properties of η-Ricci Solitons on α-Lorentzian Sasakian Manifolds

  • Shashikant, Pandey;Abhishek, Singh;Rajendra, Prasad
    • Kyungpook Mathematical Journal
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    • v.62 no.4
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    • pp.737-749
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    • 2022
  • We investigate the geometric properties of 𝜂*-Ricci solitons on α-Lorentzian Sasakian (α-LS) manifolds, and show that a Ricci semisymmetric 𝜂*-Ricci soliton on an α-LS manifold is an 𝜂*-Einstein manifold. Further, we study 𝜑*-symmetric 𝜂*-Ricci solitons on such manifolds. We prove that 𝜑*-Ricci symmetric 𝜂*-Ricci solitons on an α-LS manifold are also 𝜂*-Einstein manifolds and provide an example of a 3-dimensional α-LS manifold for the existence of such solitons.

CERTAIN RESULTS ON ALMOST KENMOTSU MANIFOLDS WITH CONFORMAL REEB FOLIATION

  • Ghosh, Gopal;Majhi, Pradip
    • Communications of the Korean Mathematical Society
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    • v.33 no.1
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    • pp.261-272
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    • 2018
  • The object of the present paper is to study some curvature properties of almost Kenmotsu manifolds with conformal Reeb foliation. Among others it is proved that an almost Kenmotsu manifold with conformal Reeb foliation is Ricci semisymmetric if and only if it is an Einstein manifold. Finally, we study Yamabe soliton in this manifold.

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.

RIEMANNIAN MANIFOLDS WITH A SEMI-SYMMETRIC METRIC P-CONNECTION

  • Chaubey, Sudhakar Kr;Lee, Jae Won;Yadav, Sunil Kr
    • Journal of the Korean Mathematical Society
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    • v.56 no.4
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    • pp.1113-1129
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    • 2019
  • We define a class of semi-symmetric metric connection on a Riemannian manifold for which the conformal, the projective, the concircular, the quasi conformal and the m-projective curvature tensors are invariant. We also study the properties of semisymmetric, Ricci semisymmetric and Eisenhart problems for solving second order parallel symmetric and skew-symmetric tensors on the Riemannian manifolds equipped with a semi-symmetric metric P-connection.

ON 3-DIMENSIONAL LORENTZIAN CONCIRCULAR STRUCTURE MANIFOLDS

  • Chaubey, Sudhakar Kumar;Shaikh, Absos Ali
    • Communications of the Korean Mathematical Society
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    • v.34 no.1
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    • pp.303-319
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    • 2019
  • The aim of the present paper is to study the Eisenhart problems of finding the properties of second order parallel tensors (symmetric and skew-symmetric) on a 3-dimensional LCS-manifold. We also investigate the properties of Ricci solitons, Ricci semisymmetric, locally ${\phi}$-symmetric, ${\eta}$-parallel Ricci tensor and a non-null concircular vector field on $(LCS)_3$-manifolds.

THE STUDY OF *-RICCI TENSOR ON LORENTZIAN PARA SASAKIAN MANIFOLDS

  • M. R. Bakshi;T. Barman;K. K. Baishya
    • Honam Mathematical Journal
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    • v.46 no.1
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    • pp.70-81
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    • 2024
  • We consider the *-general critical equation on LP Sasakian manifolds, and show that such a manifold is generalized η-Einstein. After then, we consider LP Sasakian manifolds with *-conformally semisymmetric condition, and show that such manifolds are *-Einstein. Moreover, we show that the *-conformally semisymmetric LP Sasakian manifold is locally isometric to En+1(0) × Sn(4).

ON KENMOTSU MANIFOLDS

  • JUN JAE-BOK;DE UDAY CHAND;PATHAK GOUTAM
    • Journal of the Korean Mathematical Society
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    • v.42 no.3
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    • pp.435-445
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    • 2005
  • The purpose of this paper is to study a Kenmotsu manifold which is derived from the almost contact Riemannian manifold with some special conditions. In general, we have some relations about semi-symmetric, Ricci semi-symmetric or Weyl semisymmetric conditions in Riemannian manifolds. In this paper, we partially classify the Kenmotsu manifold and consider the manifold admitting a transformation which keeps Riemannian curvature tensor and Ricci tensor invariant.

ON A CLASS OF N(κ)-QUASI EINSTEIN MANIFOLDS

  • De, Avik;De, Uday Chand;Gazi, Abul Kalam
    • Communications of the Korean Mathematical Society
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    • v.26 no.4
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    • pp.623-634
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    • 2011
  • The object of the present paper is to study N(${\kappa}$)-quasi Einstein manifolds. Existence of N(${\kappa}$)-quasi Einstein manifolds are proved. Physical example of N(${\kappa}$)-quasi Einstein manifold is also given. Finally, Weyl-semisymmetric N(${\kappa}$)-quasi Einstein manifolds have been considered.