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I saw this question on MSE. It's about the general formula of the metric of an N-sphere.

I was wondering, is there a similar general formula for the metric of an N-hyperbolic (simply connected, one-sheeted) hyperboloid? I found the case for a 2-hyperboloid (here), but I'm not able to find the general case for an N-hyperbolic hyperboloid. Can anyone offer some help with this?

Il Guercio
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  • Your definition of N-hyperbolic is unclear. Also, it is unclear which metric are you asking about, there are several. For instance, one can take the Riemannian metric induced from the ambient Euclidean space and then compute the corresponding distance function on the hyperboloid, or one can do the same using the ambient Lorentzian metric.... – Moishe Kohan Feb 26 '24 at 03:22

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