Hello! I got a quick question. The universe can have different geometries, as I understood it. And we don't need to embed these structures in any larger space, they "exist on their own" (in a mathematical sense). However my question is the following: How would one embed the hyperbolic alternative for our spatial universe in R^4? The spherical alternative seems obvious, x_1^2+x_2^2+x_3^2+x_4^2 = 1. Whats the corresponding equation for the hyperbolic geometry? Thanks!