Funk functions and constructions of dually flat Finsler metrics

Dually flat Finsler metrics arise from $\alpha$-flat information structures on Riemann—Finsler manifolds. Inspired by the theory of Funk functions and Hamel functions due to Li—Shen, we give a new approach to produce dually flat Finsler metrics in this paper. Moreover, we manufacture new dually flat spherically symmetric Finsler metrics by using the standard Euclidean norm on $\mathbb{R}^n$.