Abstract: In this paper, we study the (α, β)-metrics of constant flag curvature. We characterize almost regular (α, β)-metrics of constant flag curvature under the condition that β is a homothetic 1-form with respect to α. Furthermore, we prove that if a regular (α, β)-metric is of constant flag curvature and β is a Killing 1-form with constant length, then it must be a Riemannian metric or locally Minkowskian.

Key words: (α, β)-metric, flag curvature, S-curvature, mean Landsberg curvature, Riemannian metric, Minkowski metric, homothetic 1-form