Statistical manifolds, originally introduced by S. Amari (Differential Geometric Methods in Statistics. Lecture Notes in Statistics, vol. 28. Springer, New York, 1985), are very interesting objects originating from the geometric science of information, each point of them representing a probability distribution. Geometrically, a statistical manifold is nothing but a Riemannian manifold endowed with an additional structure consisting in a pair of torsion-free affine connections which are dual with respect to the Riemannian metric (Amari and Nagaoka, Methods of information geometry. Translations of Mathematical Monographs, vol. 191. American Mathematical Society. Oxford University Press, Oxford; 2000). Lately, due to their important applications in various fields, statistical manifolds have become a fervent topic, being investigated by numerous researchers from various scientific branches.

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CR-Submanifolds of Statistical Manifolds

  • Bang-Yen Chen,
  • Mohammad Hasan Shahid,
  • Gabriel Eduard Vilcu

摘要

Statistical manifolds, originally introduced by S. Amari (Differential Geometric Methods in Statistics. Lecture Notes in Statistics, vol. 28. Springer, New York, 1985), are very interesting objects originating from the geometric science of information, each point of them representing a probability distribution. Geometrically, a statistical manifold is nothing but a Riemannian manifold endowed with an additional structure consisting in a pair of torsion-free affine connections which are dual with respect to the Riemannian metric (Amari and Nagaoka, Methods of information geometry. Translations of Mathematical Monographs, vol. 191. American Mathematical Society. Oxford University Press, Oxford; 2000). Lately, due to their important applications in various fields, statistical manifolds have become a fervent topic, being investigated by numerous researchers from various scientific branches.