The part of the 5-flux lying in S5 doesn't have a time component, and so, it gives rise to a positive curvature.

This could give space-time a positive curvature that would not allow travel into the past.

One, is positive spatial curvature - that the universe is like a huge sphere.

Minding also raised the question whether a closed surface with constant positive curvature is necessarily rigid.

Well, balls and oranges, for example, have constant positive curvature.

It might be described as being the "opposite" of the surface of a sphere which has a positive curvature.

Even so, some slight positive curvature can be expected immediately prior to the explosion.

Next, the overall shape must have constant positive curvature.

What is the difference between negative and positive curvature?

For example, a sphere is a surface of constant positive curvature.