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arXiv · 2606.06395

Doubly Totally-Umbilical Statistical Submanifolds in the Probability Simplex

Ryu Ueno
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Abstract

We give a complete classification of doubly totally-umbilical submanifolds in the probability simplex. 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, inspired by the surface theory of Euclidean space.

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Ryu Ueno. 2026-06-04. Doubly Totally-Umbilical Statistical Submanifolds in the Probability Simplex. https://arxiv.org/abs/2606.06395

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