On compact L-reducible Finsler manifolds

The class of l-reducible finsler metric was introduced by matsumoto as a generalization of randers metrics. one open problems in finsler geometry is to find a l-reducible metric which is not of randers-type. let (m,f) be a compact 3-dimensional l-reducible metric. suppose that f has constant relatively isotropic mean landsberg curvature. then we show that f reduces to a randers metric.