Sasakian Statistical Manifolds with Semi-Symmetric Metric Connection

Year 2018, Volume: 1 Issue: 4, 226 - 232, 20.12.2018

Ahmet Kazan , Sema Kazan

https://doi.org/10.32323/ujma.439013

Cited By: 9

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

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