Some Properties of ۴-Dimensional Finsler Manifolds

In this paper, we study Cartan torsion, mean Cartan torsion and mean Landsberg curvature of ۴-dimensional Finsler metrics. First, we find the necessary and sufficient condition under which a ۴-dimensional Finsler manifold has bounded Cartan torsion and mean Cartan torsion. Then, we show that a ۴-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.

کلیدواژه ها:

Cartan torsion ، mean Cartan torsion ، mean Landsberg curvature ، Lands- berg curvature.