Amirkabir University of Technology AUT Journal of Mathematics and Computing 2783-2449 2 1 2021 02 01 On GDW-Randers metrics on tangent Lie groups 27 36 4160 10.22060/ajmc.2020.18572.1038 EN Mona Atashafrouz Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran Behzad Najafi Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran 0000-0003-2788-3360 Akbar Tayebi Department of Mathematics, Faculty of Science, University of Qom, Qom, Iran 0000-0002-6380-7624 Journal Article 2020 06 10 Let $G$ be a Lie group equipped with a left-invariant Randers metric $F$. Suppose that $F^v$ and $F^c$ denote the vertical and complete lift of $F$ on $TG$, respectively. We give the necessary and sufficient conditions under which $F^v$ and $F^c$ are generalized Douglas-Weyl metrics. Then, we characterize all 2-step nilpotent Lie groups $G$ such that their tangent Lie groups $(TG, F^c)$ are generalized Douglas-Weyl Randers metrics. Left-invariant metric Douglas metric Generalized Douglas-Weyl Metrics Randers Metric https://ajmc.aut.ac.ir/article_4160_f816dc0acface7498e10496222e9db10.pdf