一类与Funk度量射影相关的Finsler度量具有两种常曲率的条件

The Conditions for a Class of Special Finsler Metrics Projectively Related to Funk Metrics of Two Kinds of Constant Curvatures

Funk度量F是一个射影平坦的Finsler度量,它具有常曲率K=-14和常S 曲率S=12(n+1)F.首先在欧氏空间Rn的一个强凸区域Ω上用Funk度量F和闭1 形式β构造了一类新的Finsler度量 F=F+β,然后分别找到了 F具有常曲率和常S 曲率的充分必要条件.

The wellknown Funk metric F is a projectively flat Finsler metric with constant curvature K=-14 and constant Scurvature S=12(n+1)F. The authors construct a class Finsler metrics =F+β, where F and β denote Funk metric and a close lform on a strongly convex domain Ω in Rn, respectively. Then a necessary and sufficient condition for  of constant curvature and constant Scurvature is found respectively.