On a constant curvature statistical manifold

摘要: We will show that a statistical manifold $(M, g, \nabla)$ has constant curvature if and only the dual affine connection $\nabla^*$ of $\nabla$ is projectively flat $R$ connections conjugate symmetric, is, $R=R^*$, where $R^*$ $\nabla^*$. Moreover, trace-free, then above condition symmetry can be replaced by Ricci $\textit{Ric}$ $\nabla$, $\textit{Ric} = \textit{Ric}^*$. Finally, we see more fundamental than for one-parameter family connections, so-called $\alpha$-connections.