Bulletin of the
Korean Mathematical Society BKMS

In this paper, we study a class of Finsler metrics called general $\ab$-metrics, which are defined by a Riemannian metric $\a$ and a $1$-form $\b$. We show that every general $\ab$-metric with isotropic Berwald curvature is either a Berwald metric or a Randers metric. Moreover, a lot of new isotropic Berwald general $\ab$-metrics are constructed explicitly.

Keywords: Finsler metric, general $\ab$-metric, isotropic Berwald curvature, $S$-curvature

MSC numbers: 53B40, 53C60