Communications of the
Korean Mathematical Society CKMS

Given a linear connection $\nabla$ and its dual connection $\nabla^*$, we discuss the situation where $\nabla +\nabla^* = 0$. We also discuss statistical manifolds with torsion and give new examples of some type for linear connections inducing the statistical manifolds with non-zero torsion.

Keywords: Metric connection, torsion, information geometry, dual connections, statistical manifold

MSC numbers: Primary 53A35, 53B05, 53B15, 53C05, 53C80

Supported by: This work was supported by 2019 Hannam University Research Fund.