反正切Finsler度量与Kropina度量射影等价的充要条件

Sufficient and Necessary Condition for Projective Equivalence between Arctangent Finsler Metric and Kropina Metric

考虑反正切Finsler度量F=α+εβ+βarctan(β/α)和Kropina度量F=α2/β的射影等价,其中:α和α为流形M的Riemann度量;β和β为流形M非零的1-形式.利用射影等价具有相同Douglas曲率的性质,得到了这两个度量射影等价的充要条件.

We studied the projective equivalence between arctangent Finsler metric F =α＋εβ＋βarctan（β/α）and Kropina metric F=α2/βon a mainfold,whereαandαare two Riemannian metrics,and bothβandβare nonzero 1-form.Using the property that projective equivalence has the same Douglas curvature,we obtained a sufficient and necessary condition when both the metrics are projective equivalence.