Sasakian Statistical Manifolds with Semi-Symmetric Metric Connection

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.