Some Studies On Arctangent Finsler Metric

The purpose of this paper is to study a special kinds of (α,β) metrics-the arctangent Finsler metric in the form F=α+εβ+β arctan(β/α),where s=β/α,α=(?) is a Riemannian metric and β=bi(x)yi is a non-zero 1-form on the mainfold,ε is const.we discussed some properties of this finsler metric.First,we characterize projective equivalence be-tween an arctangent Finsler metric and a Kropina metric,By using the property the projective equivalence has some Douglas curvature,we ob-tain a sufficient and necessary condition when both metrics are projec-tive equivalence.Further,we prove that this kind of (α,β) metric are of isotropic S-curvature if and only if they are of isotropic mean Berwald curvature.In this case,S-curvature vanishes,i.e S=0,and they are weakly Berwald metrics.Besides,we obtained the condition that the projective flat arctangent Finsler metric is of isotropic S-curvature.