Quote by tinytim
There's space curvature, and spacetime curvature, but not time curvature on its own.[/INDENT]

Spacetime can have a curvature, which implies that time may also have a curvature. I'm still struggling with this idea, but if you start out with two synchronized clocks and after doing something, those clocks are no longer synchronized, then it could be that time has a curvature.
Another example. If we can send you in spaceship into a black hole, then we should observe you slowing down as you approach the event horizon. To you, time is not slowing down. In 10 seconds or so you’ll be gobbled up by the black hole, and some of your molecule can form a nice jet about the black holes axis of rotation.
There’s a disconnect in time. I see you slowing down as you go into the black hole, and you could see an acceleration of how the Universe evolves.