On homogeneous isotropic Berwald metrics

We study homogeneous isotropic Berwald metrics on a manifold M of dimension n⩾3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n\geqslant 3$$\end{document}. We prove that such Finsler metrics are either Randers metrics of Berwald type or Berwald metrics. This result generalises the well-known Deng–Liu theorem established for (α,β)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\alpha , \beta )$$\end{document}-metrics. It is also shown that every homogeneous isotropic Berwald metric with scalar flag curvature is either Riemannian or locally Minkowskian. As a consequence, a homogeneous isotropic Berwald metric is locally dually flat if and only if it is either a Berwald metric, or a locally Minkowskian metric of Randers type, or a Riemannian metric with negative constant sectional curvature.