Honam Mathematical Journal (호남수학학술지)

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SASAKIAN STATISTICAL MANIFOLDS WITH QSM-CONNECTION AND THEIR SUBMANIFOLDS

  • Sema Kazan (Department of Mathematics, Faculty of Arts and Sciences, Inonu University)
  • Received : 2022.12.02
  • Accepted : 2023.02.14
  • Published : 2023.09.14
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Abstract

In this present paper, we study QSM-connection (quarter-symmetric metric connection) on Sasakian statistical manifolds. Firstly, we express the relation between the QSM-connection ${\tilde{\nabla}}$ and the torsion-free connection ∇ and obtain the relation between the curvature tensors ${\tilde{R}}$ of ${\tilde{\nabla}}$ and R of ∇. After then we obtain these relations for ${\tilde{\nabla}}$ and the dual connection ∇* of ∇. Also, we give the relations between the curvature tensor ${\tilde{R}}$ of QSM-connection ${\tilde{\nabla}}$ and the curvature tensors R and R* of the connections ∇ and ∇* on Sasakian statistical manifolds. We obtain the relations between the Ricci tensor of QSM-connection ${\tilde{\nabla}}$ and the Ricci tensors of the connections ∇ and ∇*. After these, we construct an example of a 3-dimensional Sasakian manifold admitting the QSM-connection in order to verify our results. Finally, we study the submanifolds with the induced connection with respect to QSM-connection of statistical manifolds.

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References

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