In the present paper, firstly we express the relation between the semi-symmetric metric connection $\tilde{\nabla}$ and the torsion-free connection $\nabla$ and obtain the relation between the curvature tensors $\tilde{R}$ of $\tilde{\nabla}$ and $R$ of $\nabla$. After, we obtain these relations for $\tilde{\nabla}$ and the dual connection $\nabla^{\ast}.$ Also, we give the relations between the curvature tensor $\tilde{R}$ of semi-symmetric metric connection $\tilde{\nabla}$ and the curvature tensors $R$ and $R^{\ast}$ of the connections $\nabla$ and $\nabla^{\ast}$ on Sasakian statistical manifolds, respectively. We obtain the relations between the Ricci tensor (and scalar curvature) of semi-symmetric metric connection $\tilde{\nabla}$ and the Ricci tensors (and scalar curvatures) of the connections $\nabla$ and $\nabla^{\ast}.$ Finally, we construct an example of a 3-dimensional Sasakian manifold with statistical structure admitting the semi-symmetric metric connection in order to verify our results.
Sasakian Manifolds Statistical Structure Dual Connection Semi-Symmetric Metric Connection Statistical Structure
Birincil Dil | İngilizce |
---|---|
Konular | Matematik |
Bölüm | Makaleler |
Yazarlar | |
Yayımlanma Tarihi | 20 Aralık 2018 |
Gönderilme Tarihi | 29 Haziran 2018 |
Kabul Tarihi | 3 Ağustos 2018 |
Yayımlandığı Sayı | Yıl 2018 |
Universal Journal of Mathematics and Applications
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