| Shrnutí: | Let $(M,g,\varphi )$ be an $n$-dimensional locally decomposable Riemann manifold, that is, $g(\varphi X,Y)=g(X,\varphi Y)$ and $\nabla \varphi =0$, where $\nabla $ is Riemann (Levi-Civita) connection of metric $g$. In this paper, we construct a new connection on locally decomposable Riemann manifold, whose name is statistical ($\alpha ,\varphi )$-connection. A statistical $\alpha $-connection is a torsion-free connection such that $% \overline{\nabla }g=\alpha C$, where $C$ is a completely symmetric $(0,3)$% -type cubic form. The aim of this article is to use connection $\overline{% \nabla }$ and product structure $\varphi $ in the same equation, which is possible by writing the cubic form $C$ in terms of the product structure $% \varphi $. We examine some curvature properties of the new connection and give examples of it.
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