This paper studies the geometry of immersions into statistical manifolds. A necessary and sufficient condition is obtained for statistical manifold structures to be dual to each other for a non-degenerate equiaffine immersion. Then, we obtain conditions for realizing an n-dimensional statistical manifold in an \((n+1)\)-dimensional statistical manifold and its converse. Centro-affine immersion of codimension two into a dually flat statistical manifold is defined. Also, we have shown that statistical manifold realized in a dually flat statistical manifold of codimension two is conformally-projectively flat.

中文翻译：

---

沉浸在统计流形中

本文研究了浸入统计流形的几何形状。对于非退化等仿射浸入，统计流形结构彼此对偶，获得了充分必要条件。然后，我们得到在\((n+1)\)维统计流形中实现n维统计流形的条件及其逆。定义了二元二次平面统计流形的中心仿射浸入。此外，我们已经证明，在二维码二的双平坦统计流形中实现的统计流形是共形投影平坦的。