- Universal Journal of Mathematics and Applications
- Vol: 1 Issue: 4
- Sasakian Statistical Manifolds with Semi-Symmetric Metric Connection
Sasakian Statistical Manifolds with Semi-Symmetric Metric Connection
Authors : Ahmet Kazan, Sema Kazan
Pages : 226-232
Doi:10.32323/ujma.439013
View : 13 | Download : 3
Publication Date : 2018-12-20
Article Type : Research
Abstract :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.Keywords : Sasakian Manifolds, Statistical Structure, Dual Connection, Semi-Symmetric Metric Connection, Statistical Structure