Isotropic Berwald metrics are as a generalization of Berwald metrics. Shen proved that every Berwald metric is of vanishing S-curvature. In this paper, we generalize this fact and prove that every isotropic Berwald me...Isotropic Berwald metrics are as a generalization of Berwald metrics. Shen proved that every Berwald metric is of vanishing S-curvature. In this paper, we generalize this fact and prove that every isotropic Berwald metric is of isotropic S-curvature. Let F = α + β be a Randers metric of isotropic Berwald curvature. Then it corresponds to a conformal vector field through navigation representation.展开更多
In this paper, we study generalized Douglas-Weyl （α,β）-metrics. Suppose that a regular （α,β）-metric F is not of Randers type. We prove that F is a generalized Douglas-Weyl metric with vanishing S-curvature if ...In this paper, we study generalized Douglas-Weyl （α,β）-metrics. Suppose that a regular （α,β）-metric F is not of Randers type. We prove that F is a generalized Douglas-Weyl metric with vanishing S-curvature if and only if it is a Berwald metric. Moreover, by ignoring the regularity, if F is not a Berwald metric, then we find a family of almost regular Finsler metrics which is not Douglas nor Weyl. As its application, we show that generalized Douglas-Weyl square metric or Matsumoto metric with isotropic mean Berwald curvature are Berwald metrics.展开更多
We classify the almost regular weakly stretch non-Randers-type(α,β)-metrics with vanishing Scurvature.In the class of regular metrics,they reduce to Berwald ones.Here,we demonstrate that when an almost regular weakl...We classify the almost regular weakly stretch non-Randers-type(α,β)-metrics with vanishing Scurvature.In the class of regular metrics,they reduce to Berwald ones.Here,we demonstrate that when an almost regular weakly stretch non-Randers-type(α,β)-metric with vanishing S-curvature is not Berwaldian,then it is a weakly generalized unicorn.This yields an extension of Zou-Cheng and Chen-Liu’s theorems.Finally,we show that any projective non-Randersβ-change of a unicorn is a unicorn.展开更多
文摘Isotropic Berwald metrics are as a generalization of Berwald metrics. Shen proved that every Berwald metric is of vanishing S-curvature. In this paper, we generalize this fact and prove that every isotropic Berwald metric is of isotropic S-curvature. Let F = α + β be a Randers metric of isotropic Berwald curvature. Then it corresponds to a conformal vector field through navigation representation.
文摘In this paper, we study generalized Douglas-Weyl （α,β）-metrics. Suppose that a regular （α,β）-metric F is not of Randers type. We prove that F is a generalized Douglas-Weyl metric with vanishing S-curvature if and only if it is a Berwald metric. Moreover, by ignoring the regularity, if F is not a Berwald metric, then we find a family of almost regular Finsler metrics which is not Douglas nor Weyl. As its application, we show that generalized Douglas-Weyl square metric or Matsumoto metric with isotropic mean Berwald curvature are Berwald metrics.
文摘We classify the almost regular weakly stretch non-Randers-type(α,β)-metrics with vanishing Scurvature.In the class of regular metrics,they reduce to Berwald ones.Here,we demonstrate that when an almost regular weakly stretch non-Randers-type(α,β)-metric with vanishing S-curvature is not Berwaldian,then it is a weakly generalized unicorn.This yields an extension of Zou-Cheng and Chen-Liu’s theorems.Finally,we show that any projective non-Randersβ-change of a unicorn is a unicorn.
