Generalized (?, ?)-measure With Reversible Geodesic

Finsler geometry is a metric geometry which is more extensive than Rieman-n geometry.The most important class of curves,that is,geodesics,on Riemanni-an manifolds have been generalized to Finsler manifolds.They preserve the local shortest property of geodesics.However,the reversibility of geodesics have been changed because of the nonlinearity of Finsler metrics.In this paper,we focus on the characterization of Finsler metrics with reversible geodesics.In particular,when? is a closed 1-form,we give an equivalent characterization of a class of general(?,?)-metrics with reversible geodesics.