The generalized conjugate connections on semi-Riemannian manifolds are studied in this paper. A fact that an affine connection is equiaffine iff it's conjugate connection is equiaffine on statistical manifolds was generalized to the case of generalized conjugate connections on semi-Riemannian manifolds in [3]. The facts that the conjugate symmetry and conjugate Ricci-symmetry of statistical manifolds are sufficient conditions for α-connections to be equiaffine for any $\alpha (\in \mathit{R})$ are generalized to the case of generalized conjugate connections on semi-Riemannian manifolds in this paper.

中文翻译：

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半黎曼流形上的广义共轭连接和等仿射结构

本文研究了半黎曼流形上的广义共轭连接。仿射连接是等仿射的，当它的共轭连接在统计流形上是等仿射的，这一事实被推广到 [3] 中半黎曼流形上的广义共轭连接的情况。统计流形的共轭对称性和共轭 Ricci 对称性是α-连接对任何方程等仿射的充分条件。$\alpha (\in \mathit{电阻})$ 推广到本文中半黎曼流形上的广义共轭连接的情况。