the effect of curveture on space-time

[Blissfulpain]

our current universe has no curve to it, this means that parallel lines stay parallel to the extent of infinity. suppose there was a universe that had a negative curve to it... this cause parallel lines to eventually intersect... what i am not clear on is if these lines would not only join at the extent of infinity, but actually cross over each other and continue on thereafter diverging farther and farther away.

any other effects of space curveture you can think of would also be neat to know, thx

[pervect]

Negative curvature would be a saddle surface, sometimes called a hyperbolic geometry. Parallel lines would not intersect, and there are an infinite number of lines parallel to another that pass through a given point.

See for instance

http://education.yahoo.com/reference/encyclopedia/entry?id=34192