A class of Finsler metrics with conformal radical fields

Abstract

Let $F$ be a Finsler metric on an open subset $\mathcal{U}$ in $\mathbb{R}^n$. By finding a necessary and sufficient condition equivalent to the radical field on $\mathcal{U}$ being conformal with respect to $F$ we completely determine spherically symmetric Finsler metrics on $\mathcal{U}$ whose radical field is conformal. We show that for these Finsler metrics, their tangent spaces are linearly isometric to each other as in the Berwald case.