Sasakian Statistical Manifolds with Semi-Symmetric Metric Connection

Authors : Ahmet KAZAN, Sema KAZAN

Pages : 226-232

Doi:10.32323/ujma.439013

View : 21 | Download : 4

Publication Date : 2018-12-20

Article Type : Research Paper

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 insert ignore into journalissuearticles values(and scalar curvature); of semi-symmetric metric connection $\tilde{\nabla}$ and the Ricci tensors insert ignore into journalissuearticles values(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