Some Properties of 4-Dimensional Finsler Manifolds

In this paper, we study Cartan torsion, mean Cartan torsion and mean Landsberg curvature of 4-dimensional Finsler metrics. First, we find the necessary and sufficient condition under which a 4-dimensional Finsler manifold has bounded Cartan torsion and mean Cartan torsion. Then, we show that a 4-dimensional Finsler manifold has relatively isotropic mean Landsberg curvature if and only if it is Riemannian or the main scalars of Finsler metric satisfy the certain conditions.