Seeking definition

Can anyone help me track down a fairly straightforward dictionary definition of "Curved Space" or "Curved spaces" I'm assuming most will be scientific, but any slightly more metaphysical ones could work too.

(Need a quote for a central image on my website now I've finally (nearly) got my portfolio up online)

EDIT: Following Keef's wonderful off-the-top-of-his-head summary, I'd also welcome any personal definitions of descriptions of what you understand the term "curved spaces" to mean, be it serious, surreal or just plain stupid!