Equiaffine structure and conjugate Ricci-symmetry of a statistical manifold

作者: Cholrim Min , Wonhak Ri , Kumhyok Kwak , Dokjun An

DOI: 10.1016/J.DIFGEO.2015.04.005

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摘要: Abstract A condition for a statistical manifold to have an equiaffine structure is studied. The facts that dual flatness and conjugate symmetry of are sufficient conditions were obtained in [4] [5] . In this paper, fact manifold, which Ricci-symmetric, has given, where Ricci-symmetry weaker than symmetry. coincide also given.

参考文章(5)
J.-i. Takeuchi, S.-i. Amari, /spl alpha/-parallel prior and its properties IEEE Transactions on Information Theory. ,vol. 51, pp. 1011- 1023 ,(2005) , 10.1109/TIT.2004.842703
Shun-ichi Amari, Hiroshi Nagaoka, Methods of information geometry ,(2000)
Takashi Kurose, Dual connections and affine geometry Mathematische Zeitschrift. ,vol. 203, pp. 115- 121 ,(1990) , 10.1007/BF02570725
Hiroshi Matsuzoe, Jun-ichi Takeuchi, Shun-ichi Amari, Equiaffine structures on statistical manifolds and Bayesian statistics Differential Geometry and its Applications. ,vol. 24, pp. 567- 578 ,(2006) , 10.1016/J.DIFGEO.2006.02.003
Jun Zhang, A note on curvature of α-connections of a statistical manifold Annals of the Institute of Statistical Mathematics. ,vol. 59, pp. 161- 170 ,(2007) , 10.1007/S10463-006-0105-1