On D-Recurrent Finsler Metrics


In this paper, we study D-recurrent Finsler metrics and characterize D-recurrent Randers metrics. Indeed, we show that a Randers metric \(F=\alpha +\beta \) is D-recurrent if and only if \(\mathrm{d}\beta \) is nearly recurrent. We prove that a GDW-Randers metric is a Douglas metric provided that it is D-recurrent. Then, we extend this fact to all the Finsler metrics: GDW-metrics are Douglas metric if they are D-recurrent. Then, we show that in the class of spherically symmetric Finsler metrics, Douglas metrics coincide with D-recurrent ones.

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We thank the referee for his/her valuable suggestions and comments.

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Correspondence to Behzad Najafi.

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Communicated by Mohammad Koushesh .

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Atashafrouz, M., Najafi, B. On D-Recurrent Finsler Metrics. Bull. Iran. Math. Soc. 47, 143–156 (2021). https://doi.org/10.1007/s41980-020-00372-y

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  • D-recurrent
  • Douglas metrics
  • Spherically symmetric metrics

Mathematics Subject Classification

  • 53B40
  • 53C60