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Determining hyperbolic or euclidean geometry
Consider the Riemmanian product metric:
$$ ds^2= f(\theta)~d\theta^2 + f(r)~dr^2$$
for $\theta, r>0$ and $f(\theta)=2\sqrt{\theta}K_1(2\sqrt{\theta})$ where $K_1$ is a modified Bessel function.
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