统计流形的等仿射结构与共轭Ricci对称性
Equiaffine Structure and Conjugate Ricci-symmetry of a Statistical Manifold
摘要：
研究了统计流形具有等仿射结构的条件。文[2]和[3]得到了统计流形的对偶平坦性和共轭对称性是统计流形具有等仿射结构的充分条件。本文证明了共轭Ricci对称的统计流形具有等仿射结构，其中共轭Ricci对称是比共轭对称弱的条件。给出了共轭对称性与共轭Ricci对称性重合的条件。
英文摘要：
A condition for a statistical manifold to have an equiaffine structure is studied. The facts that dual flatness and conjugate symmetry of a statistical manifold are sufficient conditions for a statistical manifold to have an equiaffine structure were obtained in [2] and [3]. In this paper, a fact that a statistical manifold, which is conjugate Ricci-symmetric, has an equiaffine structure is given, where conjugate Ricci-symmetry is weaker condition than conjugate symmetry. A condition for conjugate symmetry and conjugate Ricci-symmetry to coincide is also given.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
