SOME PROPERTIES OF 4-DIMENSIONAL FINSLER MANIFOLDS

Document Type : Original Article

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Abstract
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.

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