Sasakian Statistical Manifolds with Semi-Symmetric Metric Connection

Abstract

In the present paper, firstly we express the relation between the semi-symmetric metric con-nection∇ and the torsion-free connection ∇ and obtain the relation between the curvature tensorsR of∇ and R of ∇. After, we obtain these relations for∇ and the dual connection ∇ *. Also, we give the relations between the curvature tensorR of semi-symmetric metric connection∇ and the curvature tensors R and R * of the connections ∇ and ∇ * on Sasakian statistical manifolds, respectively. We obtain the relations between the Ricci tensor (and scalar curvature) of semi-symmetric metric connection∇ and the Ricci tensors (and scalar curvatures) of the connections ∇ and ∇ *. 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.

Lifts of a Semi-Symmetric Metric Connection from Sasakian Statistical Manifolds to Tangent Bundle

“…holds for any vector fields X 0 and Y 0 on M [6]. In a statistical structure ( ∇, g 0 ) and an almost-contact metric structure (g 0 , Φ 0 , A) on M, the structure ( ∇, g 0 , Φ 0 , A) is known as a Sasakian statistical structure if and only if it satisfies the following formulas [9,27]:…”

“…Kurose [8] studied the concept of the holomorphic statistical structure as a generalization of Kahler's structure. Kazan and Kazan [9] investigated the SSMC on Sasakian statistical manifolds. In [10,11], the authors investigated connections on statistical manifolds.…”

Casorati Inequalities for Statistical Submanifolds in Kenmotsu Statistical Manifolds of Constant ϕ-Sectional Curvature with Semi-Symmetric Metric Connection

“…According to Kazan et al [ 38 ], the relations between the curvature tensor of and the curvature tensors and of the connections and are as follows: and for any .…”

“…However, only a few results are dedicated to the ambient of statistical manifolds endowed with semi-symmetric metric connection. S. Kazan and A. Kazan obtained some geometric properties of Sasakian statistical manifolds with a semi-symmetric metric connection [ 38 ]. Furthermore, M.B.K.…”

Anti-invariant ξ⊥-cosymplectic-like statistical submersions

“…Kazan [10], the author has studied conformally-projectively flat trans-Sasakian statistical manifolds. Also, the authors have examined Sasakian statistical manifolds with semi-symmetric metric connection in [11].…”