Abstract
We prove a rigidity result for homogeneous generalized Douglas–Weyl metrics of Landsberg-type. We show that such metrics have constant \(\mathbf{H}\)-curvature along geodesics. Then, we prove that every homogeneous D-recurrent Finsler metric is a Douglas metric. It turns out that a homogeneous D-recurrent \((\alpha , \beta )\)-metric is a Randers metric or Berwaldian metric, generalizing the result known only in the case of Douglas metrics. Finally, we show that homogeneous generalized isotropic L-reducible metrics are Randers metrics or L-reducible metrics.
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Communicated by M. Reza Koushesh.
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Kamelaei, F., Tayebi, A. & Najafi, B. On Homogeneous Finsler Manifolds with Some Curvature Properties. Bull. Iran. Math. Soc. 48, 2685–2697 (2022). https://doi.org/10.1007/s41980-021-00664-x
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DOI: https://doi.org/10.1007/s41980-021-00664-x