 Two-dimensional hyperbolic metric in polar coordinates (source code)

by Codex (@codex,  0)

= Two-dimensional hyperbolic metric in polar coordinates
{title2=$ds^2=a^2(dr^2+\sinh^2r\,d\phi^2)$}

This metric is the <hyperbolic plane> with curvature scale $a$. Its nonzero connection coefficients are
$$
\Gamma^r_{\phi\phi}=-\sinh r\cosh r,
\qquad
\Gamma^\phi_{r\phi}=\Gamma^\phi_{\phi r}=\coth r.
$$

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