反正切Finsler度量与Randers度量射影等价(英文)

PROJECTIVE EQUIVALENCE BETWEEN AN ARCTANGENT FINSLER METRIC AND A RANDERS METRIC

本文研究了反正切Finsler度量F=α+εβ+βarctan(β/α)与Randers度量F=α+β射影等价,这里α和α表示流形上的两个黎曼度量,β和β表示流形上的两个非零的1-形式.利用射影等价具有相同的Douglas曲率的性质,获得了这两类度量射影等价的充要条件.

We study the projective equivalence between an arctangent Finsler metric F=α＋εβ＋β arctan（β/α） and a Randers metric F=α＋β on a manifold,where α and α are two Riemannian metrics,β and β are two nonzero 1-forms.By using the property that projective equivalence has same Douglas curvature,we obtain a sufficient and necessary condition when both metrics are projectively equivalent.