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On Generalized Douglas-Weyl Randers Metrics

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Abstract

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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Acknowledgments

The authors are grateful to Zhongmin Shen for his valuable comments during completing this paper. The authors would like to thank the referee for his/her valuable suggestions.

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Authors and Affiliations

  1. Amirkabir University of Technology, Tehran Polytechnic, Rasht St, Tehran, Iran

    Tayebeh Tabatabaeifar & Behzad Najafi

  2. University of Mazandaran, Pasdaran St, Babolsar, Mazandaran, Iran

    Mehdi Rafie-Rad

Authors
  1. Tayebeh Tabatabaeifar
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  2. Behzad Najafi
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  3. Mehdi Rafie-Rad
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Correspondence to Behzad Najafi.

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Tabatabaeifar, T., Najafi, B. & Rafie-Rad, M. On Generalized Douglas-Weyl Randers Metrics. Czech Math J 71, 155–172 (2021). https://doi.org/10.21136/CMJ.2020.0241-19

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