芬斯勒射影几何中的Ricci曲率(英文)

THE RICCI CURVATURE IN FINSLER PROJECTIVE GEOMETRY

本文研究了保持Ricci曲率不变的Finsler射影变换。给定一个紧致无边的n维可微流形M,证明了:对于一个从M上的Berwald度量到Riemann度量的C射影变换,如果Berwald度量的Ricci曲率关于Riemann度量的迹不超过Riemann度量的标量曲率,则该射影变换是平凡的。

In this paper we first study the Finsler projective change which preserves the Ricci curvature. Furthermore,given a compact and boundaryless n-dimensional differentiable manifold M, we show that any pointwise C-projective change from a Berwald space （M,F） to a Riemann space （M,F） is trivial if the trace of the Ricci curvature Ric of F with respect to F is less or equal to the scalar curvature of F.