Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Left Invariant Randers Metrics of Berwald type on Tangent Lie Groups   Let $G$ be a Lie group equipped with a left invariant Randers metric of
Berward type $F$, with underlying left invariant Riemannian metric $g$. Suppose
that $\widetilde{F}$ and $\widetilde{g}$ are lifted Randers and Riemannian
metrics arising from $F$ and $g$ on the tangent Lie group $TG$ by vertical and
complete lifts. In this article we study the relations between the flag
curvature of the Randers manifold $(TG,\widetilde{F})$ and the sectional
curvature of the Riemannian manifold $(G,g)$ when $\widetilde{F}$ is of Berwald
type. Then we give all simply connected $3$-dimentional Lie groups such that
their tangent bundles admit Randers metrics of Berwarld type and their
geodesics vectors.

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The categories of this paper are: supr-con
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The categories of this paper are: hep-lat
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
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The categories of this paper are: nlin
7
The categories of this paper are: hep-th
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The categories of this paper are: gr-qc
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The categories of this paper are: quant-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: patt-sol
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The categories of this paper are: eess