某类Finsler-Einstein空间之间的共形映射

摘要

Liouville定理证明了欧氏空间到自身的共形变换是莫比乌斯变换.关于Riemann空间,Brinkmann首先得到了一般的结论.但对Finsler空间的研究乏人问津.本文运用导航术和共形映射的性质证明了Randers空间(或Kropina空间)之间保Einstein度量的共形变换必是相似变换.%Liouville's Theorem proved that the Euclidean space can be mapped conformally on itself only by a composition of M(o)bius transformations.For Riemann spaces,Brinkmann obtained general results.Little work has been done on Finsler spaces.This paper,by navigation idea and properties of conformal map,proved that the conformal transformation between Einstein Randers (or Kropina) spaces must be homothetic.