On Landsberg general (α,β)-metrics with a conformal 1-form

In this paper, we study almost regular Landsberg general (α,β)-metrics in Finsler geometry. The corresponding equivalent equations are given. By solving the equations, we derive the two cases of Landsberg general (α,β)-metrics under the condition that β is closed and conformal with respect to α. Under this condition, we prove that regular Landsberg general (α,β)-metrics must be Berwaldian when the dimension is greater than two. For the almost regular case, the way to construct non-Berwaldian Landsberg metrics is found and some new explicit examples are constructed.