On GDW-Randers metrics on tangent Lie groups

Document Type : Original Article


1 Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran

2 Department of Mathematics, Faculty of Science, University of Qom, Qom, Iran



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.


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