Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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η-RICCI SOLITONS ON TRANS-SASAKIAN MANIFOLDS WITH QUARTER-SYMMETRIC NON-METRIC CONNECTION

  • Bahadir, Oguzhan (Department of Mathematics, Faculty of Science and Letters, Kahramanmaras Sutcu Imam University) ;
  • Siddiqi, Mohd Danish (Department of Mathematics Faculty of Science, Jazan University) ;
  • Akyol, Mehmet Akif (Department of Mathematics, Faculty of Arts and Sciences, Bingol University)
  • Received : 2020.04.14
  • Accepted : 2020.06.09
  • Published : 2020.09.25
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Abstract

In this paper, firstly we discuss some basic axioms of trans Sasakian manifolds. Later, the trans-Sasakian manifold with quarter symmetric non-metric connection are studied and its curvature tensor and Ricci tensor are calculated. Also, we study the η-Ricci solitons on a Trans-Sasakian Manifolds with quartersymmetric non-metric connection. Indeed, we investigated that the Ricci and η-Ricci solitons with quarter-symmetric non-metric connection satisfying the conditions ${\tilde{R}}.{\tilde{S}}$ = 0. In a particular case, when the potential vector field ξ of the η-Ricci soliton is of gradient type ξ = grad(ψ), we derive, from the η-Ricci soliton equation, a Laplacian equation satisfied by ψ. Finally, we furnish an example for trans-Sasakian manifolds with quarter-symmetric non-metric connection admitting the η-Ricci solitons.

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References

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