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I found this metric in an exercise sheet from a Riemannian Geometry Course. Let be the following metric $$g_{ij}=\left(\begin{array}{ccc} 1 & 0 & \sin\vartheta\\ 0 & 1 & 0\\ \sin\vartheta & 0 & 1 \end{array}\right),$$ defined om $$ U=\left\{ \left(\psi,\,\vartheta,\,\phi\right)\in\mathbb{R}^{3}\,:\,\theta\neq\frac{\pi}{2}+k\pi\right\}.$$

I suspect is something taken (maybe with some alteration) from something known in General Relativity. Does anybody knows somethign about it? It's a really nice example for a lot of stuff and I would like to use it for some lecture notes...

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