In what ways are the fate of the universe, the shape of the universe, and the average density of the universe related

Based on our science, the universe could have three possible shapes dependant on the amount of matter in it, the matter affects the curvature of the universe, linked to its shape and geometry. For example, a closed Universe will have a positive curvature, meaning that the average density is more than the critical density. An open universe, on the other hand, would have a negative curvature, and therefore the qaverage density would be less than the critical density. A flat universe would have no curvature and the average density would be equal to the critical density. These shapes relate to the fate of the universe, a closed universe would be finite, an open universe would be infinite and a flat universe would be infinite with no curve.