共形平坦且具有弱迷向S曲率的(α,β)度量的分类

The classification of( α,β)-metrics with conformal flat and weak isotropic S curvature

将黎曼流形上共形平坦结果推广到Finsler流形上。研究(α,β)度量的共形平坦问题,建立(α,β)度量上的特殊坐标系,得到具有弱迷向S曲率且共形平坦的(α,β)度量的性质,给出此时(α,β)度量的分类,即对共形平坦且弱迷向S曲率的(α,β)度量或是黎曼度量或是Minkowski度量。

In order to generalize the results of conformal flatness on Riemannian manifolds to Finsler manifolds, the problem of conformal flatness of （α,β） -metrics is studied. Utilizing the special coordinate system on（α,β）-metrics, the properties of （α,β）-metrics with conformal fiat and weak isotropic S curvature are obtained, and the classification of （α,β）-metrics is given, that is, （α,β）-metrics with conformal flat and weak isotropic curvature S curvature is Riemannian metric or Minkowski metric.