Geodesic
On generalized Douglas-Weyl Randers metrics
Czechoslovak Mathematical Journal, Tome 71 (2021) no. 1, pp. 155-172
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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.
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.
DOI : 10.21136/CMJ.2020.0241-19
Classification : 53B40, 53C60
Keywords: generalized Douglas-Weyl metric; Randers metric; Kenmotsu manifold; Sasakian manifold 
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Tabatabaeifar, Tayebeh; Najafi, Behzad; Rafie-Rad, Mehdi. On generalized Douglas-Weyl Randers metrics. Czechoslovak Mathematical Journal, Tome 71 (2021) no. 1, pp. 155-172. doi: 10.21136/CMJ.2020.0241-19

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