摘要
In this paper, we study a significant non-Riemannian quantity E-curvature, which is defined by S-curvature. Firstly, we obtain the formula of E-curvature for （α,β）-metrics. Based on it, we show that the E-curvature vanishes for a class of （α,β）-metrics. In the end, we get the relation of E-curvature for conformally related Finsler metrics, and classify conformally flat （α,β）-metries with almost vanishing E-curvature.
In this paper, we study a significant non-Riemannian quantity E-curvature, which is defined by S-curvature. Firstly, we obtain the formula of E-curvature for （α,β）-metrics. Based on it, we show that the E-curvature vanishes for a class of （α,β）-metrics. In the end, we get the relation of E-curvature for conformally related Finsler metrics, and classify conformally flat （α,β）-metries with almost vanishing E-curvature.
基金
Supported by National Natural Science Foundation of China(Grant No.11371386)
the European Union’s Seventh Framework Programme(FP7/2007-2013)(Grant No.317721)
