论文标题
在恒定的曲率统计歧管上
On a constant curvature statistical manifold
论文作者
论文摘要
We will show that a statistical manifold $(M, g, \nabla)$ has a constant curvature if and only if it is a projectively flat conjugate symmetric manifold, that is, the affine connection $\nabla$ is projectively flat and the curvatures satisfies $R=R^*$, where $R^*$ is the curvature of the dual connection $\nabla^*$.此外，我们将表明，在投影平坦的紧凑型歧管上正确凸结构会诱导恒定曲率$ -1 $统计结构，反之亦然。
We will show that a statistical manifold $(M, g, \nabla)$ has a constant curvature if and only if it is a projectively flat conjugate symmetric manifold, that is, the affine connection $\nabla$ is projectively flat and the curvatures satisfies $R=R^*$, where $R^*$ is the curvature of the dual connection $\nabla^*$. Moreover, we will show that properly convex structures on a projectively flat compact manifold induces constant curvature $-1$ statistical structures and vice versa.
