I How to embed the universe in R^4

[Kontilera]

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!

 

[Khashishi]

$x_1^2 - x_2^2 - x_3^2 -x_4^2 = 1$
But note that you must calculate distance in a funny way. https://en.wikipedia.org/wiki/Hyperboloid_model