Doubly autoparallel structure on the probability simplex

Atsumi Ohara; Hideyuki Ishi

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arXiv · 1711.11456

Doubly autoparallel structure on the probability simplex

Atsumi Ohara·Hideyuki Ishi

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Abstract

On the probability simplex, we can consider the standard information geometric structure with the e- and m-affine connections mutually dual with respect to the Fisher metric. The geometry naturally defines submanifolds simultaneously autoparallel for the both affine connections, which we call {\em doubly autoparallel submanifolds}. In this note we discuss their several interesting common properties. Further, we algebraically characterize doubly autoparallel submanifolds on the probability simplex and give their classification.

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Atsumi Ohara, Hideyuki Ishi. 2017-11-30. Doubly autoparallel structure on the probability simplex. https://arxiv.org/abs/1711.11456

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