We characterize generalized Douglas-Weyl Randers metrics in terms of their Zermelo navigation data. Then, we study the Randers metrics induced by some important classes of almost contact metrics. Furthermore, we construct a family of generalized Douglas-Weyl Randers metrics which are not R-quadratic. We show that the Randers metric induced by a Kenmotsu manifold is a Douglas metric which is not of isotropic S-curvature. We show that the Randers metric induced by a Kenmotsu or Sasakian manifold is not Einsteinian. By using D-homothetic deformation of a Kenmotsu or Sasakian manifold, we construct a family of generalized Douglas-Weyl Randers metrics and show that the Lie group of projective transformations does not act transitively on the set of generalized Douglas-Weyl Randers metrics.

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关于广义 Douglas-Weyl Randers 度量

我们根据 Zermelo 导航数据描述了广义的 Douglas-Weyl Randers 指标。然后，我们研究了一些重要类别的几乎接触度量引起的兰德斯度量。此外，我们构建了一系列非 R 二次型的广义 Douglas-Weyl Randers 度量。我们表明由 Kenmotsu 流形引起的兰德斯度量是一个道格拉斯度量，它不是各向同性的 S 曲率。我们表明由 Kenmotsu 或 Sasakian 流形引起的兰德斯度量不是爱因斯坦的。通过使用 Kenmotsu 或 Sasakian 流形的 D 同位变形，我们构建了一系列广义 Douglas-Weyl Randers 度量，并表明射影变换的李群不会对广义 Douglas-Weyl Randers 度量集合起作用。