  In this paper, we prove that every homogeneous Landsberg surface has
isotropic flag curvature. Using this special form of the flag curvature, we
prove a rigidity result on homogeneous Landsberg surface. Indeed, we prove that
every homogeneous Landsberg surface is Riemannian or locally Minkowskian. This
gives a positive answer to the Xu-Deng's well-known conjecture in 2-dimensional
homogeneous Finsler manifolds.
