Toric dually flat manifolds and complex space forms

TL;DR

This paper classifies 1-dimensional connected dually flat manifolds that are toric and demonstrates that their torifications are complex space forms, with particular focus on exponential families over finite sets.

Contribution

It provides a classification of 1D toric dually flat manifolds and links their torifications to complex space forms, especially for exponential families over finite sets.

Findings

Toric dually flat manifolds are classified in 1D.

Their torifications are shown to be complex space forms.

Special case analysis for exponential families over finite sets.

Abstract

We classify 1-dimensional connected dually flat manifolds $M$ that are toric in the sense of [Molitor, arXiv:2109.04839], and show that the corresponding torifications are complex space forms. Special emphasis is put on the case where M is an exponential family defined over a finite set.