Doubly autoparallel structure on the probability simplex
Differential Geometry
2017-12-01 v1
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.
Cite
@article{arxiv.1711.11456,
title = {Doubly autoparallel structure on the probability simplex},
author = {Atsumi Ohara and Hideyuki Ishi},
journal= {arXiv preprint arXiv:1711.11456},
year = {2017}
}