Riemann-Finsler几何中的若干问题

Several problems in Riemann-Finsler geometry

Finsler几何是比Riemann几何更一般的微分几何,近几十年来取得了全新的实质性进展.本文就若干尚未解决的整体Finsler几何问题作一概要的综述,主要涉及Finsler子流形几何、Finsler流形的曲率和拓扑,以及Finsler-Einstein度量.

In differential geometry,Finsler geometry is more general than Riemannian geometry,which has been developed essentially in recent decades. In this paper,some open problems in global Finsler geometry are summarized briefly. Such problems deal with Finsler submanifolds,the curvature and topology of Finsler manifolds,and Finsler-Einstein metrics.