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Riemannian metrics – left, right and bi-invariant
The discussion in this post applies to Riemannian metrics on Lie groups in general, but we will concentrate on just one case in hand: SL(2,R). Let $G$ be a Lie group. Vectors tangent to paths in $G,$ at identity $e\in G$ form the Lie algebra of the group. Usually it is denoted by $\mathrm{Lie}(G).
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Riemannian metrics – left, right and bi-invariant
The discussion in this post applies to Riemannian metrics on Lie groups in general, but we will concentrate on just one case in hand: SL(2,R). Let $G$ be a Lie group. Vectors tangent to paths in $G,$ at identity $e\in G$ form the Lie algebra of the group. Usually it is denoted by $\mathrm{Lie}(G).
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Riemannian metrics – left, right and bi-invariant
The discussion in this post applies to Riemannian metrics on Lie groups in general, but we will concentrate on just one case in hand: SL(2,R). Let $G$ be a Lie group. Vectors tangent to paths in $G,$ at identity $e\in G$ form the Lie algebra of the group. Usually it is denoted by $\mathrm{Lie}(G).
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- descriptionThe discussion in this post applies to Riemannian metrics on Lie groups in general, but we will concentrate on just one case in hand: SL(2,R). Let $G$ be a Lie group. Vectors tangent to paths in $G,$ at identity $e\in G$ form the Lie algebra of the group. Usually it is denoted by $\mathrm{Lie}(G).
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