# What would it look like to be inside a small space with positive curvature?

Say you're floating in an empty void with a light source. The space you are in has a positive curvature, so going forwards will bring you back to the place you started after about 20 meters. What do you see?

Bonus question: Is this similar to being on the surface of a hyper-sphere? If you're on the edge of a circle, there is one dimension to move along and eventually you will come back to where you came from. If you're on the surface of a sphere there are two dimensions to move along, and if you go in one direction for long enough you'll come back to the start as well. I'm thinking there should be an analogue for a 4D-sphere where you can move along 3 dimensions.

• What do you see? - a space that highly curved would have a huge matter/energy density and would be expanding or contracting at an extreme rate. You can't just move 20m to get back to your starting point because the universe would be expanding away from you faster than you could move. The same applies to light rays. – John Rennie May 28 at 8:21
• @JohnRennie: You could cook up an unstable equilibrium, depending on the types of matter fields present. – Ben Crowell May 28 at 12:16
• @BenCrowell then put a human in it and expect it to stay stable? – John Rennie May 28 at 13:16