• Title/Summary/Keyword: semi-symmetric metric P-connection

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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.

STUDY OF GRADIENT SOLITONS IN THREE DIMENSIONAL RIEMANNIAN MANIFOLDS

  • Biswas, Gour Gopal;De, Uday Chand
    • Communications of the Korean Mathematical Society
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    • v.37 no.3
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    • pp.825-837
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    • 2022
  • We characterize a three-dimensional Riemannian manifold endowed with a type of semi-symmetric metric P-connection. At first, it is proven that if the metric of such a manifold is a gradient m-quasi-Einstein metric, then either the gradient of the potential function 𝜓 is collinear with the vector field P or, λ = -(m + 2) and the manifold is of constant sectional curvature -1, provided P𝜓 ≠ m. Next, it is shown that if the metric of the manifold under consideration is a gradient 𝜌-Einstein soliton, then the gradient of the potential function is collinear with the vector field P. Also, we prove that if the metric of a 3-dimensional manifold with semi-symmetric metric P-connection is a gradient 𝜔-Ricci soliton, then the manifold is of constant sectional curvature -1 and λ + 𝜇 = -2. Finally, we consider an example to verify our results.

ON A SEMI-SYMMETRIC METRIC CONNECTION IN AN (ε)-KENMOTSU MANIFOLD

  • Singh, Ram Nawal;Pandey, Shravan Kumar;Pandey, Giteshwari;Tiwari, Kiran
    • Communications of the Korean Mathematical Society
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    • v.29 no.2
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    • pp.331-343
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    • 2014
  • The object of the present paper is to study a semi-symmetric metric connection in an (${\varepsilon}$)-Kenmotsu manifold. In this paper, we study a semi-symmetric metric connection in an (${\varepsilon}$)-Kenmotsu manifold whose projective curvature tensor satisfies certain curvature conditions.

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.