On Homogeneous Finsler Manifolds with Some Curvature Properties

We prove a rigidity result for homogeneous generalized Douglas–Weyl metrics of Landsberg-type. We show that such metrics have constant H-curvature along geodesics. Then, we prove that every homogeneous D-recurrent Finsler metric is a Douglas metric. It turns out that a homogeneous D-recurrent (α, β)-metric is a Randers metric or Berwaldian metric, generalizing the result known only in the case of Douglas metrics. Finally, we show that homogeneous generalized isotropic L-reduciblemetrics are Randers metrics or L-reducible metrics.