The effect of curveture on space-time

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In a universe with no curvature, parallel lines remain parallel indefinitely. Conversely, a universe with negative curvature, resembling a saddle shape, allows for multiple parallel lines to exist through a single point without intersecting. The discussion raises questions about whether lines in such a universe could eventually cross and then diverge. Additionally, the effects of space curvature on geometry, particularly hyperbolic geometry, are highlighted. Understanding these concepts is crucial for grasping the implications of curvature on the nature of 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
 
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