A note on curvature of α-connections of a statistical manifold
A note on curvature of α-connections of a statistical manifold
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DOI：
10.1007/s10463-006-0105-1
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发表时间：
2007-02
影响因子：
1
通讯作者：
Jun Zhang
中科院分区：
文献类型：
--
作者：
Jun Zhang
在一个统计流形上，有一对共轭连通和，其α-连通族<$（α）被给出为。在这里，我们给出了曲率R（α）的表达式，其中R（α）与α的曲率R（α）有关。从它可以直接看出，对于对偶平坦的任何时候，都是等仿射的，正如Takeuchi和Amari（IEEE Transactions on Information Theory 51：1011-1023，2005）所观察到的那样。并给出了其它相关公式。
The family of α-connections ∇(α)on a statistical manifoldequipped with a pair of conjugate connectionsandis given as. Here, we develop an expression of curvatureR(α)for ∇(α)in relation to those for. Immediately evident from it is that ∇(α)is equiaffine for anywhenare dually flat, as previously observed in Takeuchi and Amari (IEEE Transactions on Information Theory51:1011–1023, 2005). Other related formulae are also developed.