Doubly Totally-Umbilical Statistical Submanifolds in the Probability Simplex
Abstract
The probability simplex is one of the most standard statistical manifolds, and information geometry initiated by S. Amari and H. Nagaoka studies the statistical submanifold theory of the probability simplex. On the other hand, H. Furuhata defined doubly totally-umbilical submanifolds in the geometry of statistical manifolds. We give the complete classification of doubly totally-umbilical submanifolds in the probability simplex.