# For the case where universe is not flat, has it got an extrinsic curvature towards (an)other spatial dimension(s)? [duplicate]

I got the idea that expansion of the universe is not to somewhere, it is just getting stretched of spacetime since a point of singularity. And I know that universe was calculated as flat (which means sum of angles of a triangle is exactly π ignoring local instrinsic curvatures caused by celestial masses) with a very small error rate. But still universe is possible to be hyperbolical or elliptical. If it is elliptical, when you travel on a straight route, you will eventually arrive at your starting point (we assume expansion of the universe is frozen). So, can we say that in that travel I am actually circumnavigating on the surface of a higher dimensional sphere and that means spacetime has an extrinsic curvature beside its intrinsic curvature.

• In response to your first question: walk in one direction until you return to your starting point. Divide this distance by $2\pi$. This is the radius. – bapowell Apr 3 '18 at 21:28