Yes, the inhabitants of Flatland, the two-dimensional universe, have discovered relativity. They’ve noticed that mass and accelleration causes a “curvature” of the space-time “sheet”.
They’re wondering whether that curvature is in a literal 3rd spacial dimension, or the “curvature” is merely a state description of the sheet’s properties?
Dr. Crane! Your glockenspiel has come to life!
Just a hint there, brother.
When you start thinking about this sort of thing it’s time to pop in some Jimi and read the Tao Te Ching
“Remember, the world is only just becoming literate” -Aldous Huxley
Actually, I playing Jimi and reading the Tao when the question came to my mind. 
Then you’re going to want to read some Lin Yutang and go to bed dude, cause the combination of the the 3 is gonna knock you flat for a while
“Remember, the world is only just becoming literate” -Aldous Huxley
Well, Singledad, I can see I’m going to be a spectator for this one, but while we wait for the knowledgable ones to arrive, I have just this for the Flatlanders:
"That’s for us to know and you to find out!"
So there.
I don’t see how dimensions have anything to do with relativity.
Perhaps it was Einstein’s model for gravity you were describing.
I asked the question many months before, “Do other dimensions really exist?”
I got a good answer. The 2nd dimension does exist. It exists in our shadows, and our images.
But can life exist in other dimensions? Well, I think I’ll just drink a beer and watch someone else try to answer that one.
There’s always another beer.
I don’t think the flatlanders would everr notice a curvature (though they might be able to postulate it.)
I imagine they might draw the conclusion that space/time is circular. I doubt they’d come up with curved.
“Don’t just stand there in Uffish thought!”
-The Caterpillar
The “life” that exists in Flatland is entirely metaphorical, of course.
They have noticed the phenomenon that light travels at a constant speed in every reference frame. They have deduced the laws of 2-D electromagnetism (which also predicts the constancy of the speed of light) and realize that relativity keeps those laws consistent in reference frames that are moving with respect to one another.
They have realized that all of the equations “make sense” if they postulate a third spacial dimension that their ordinary three-dimensional space-time (two spacial dimensions and one time dimension) “curves into”.
Being a very simple and straightforward explanation, they wonder: should this “curvature” interpretation be considered literally true?
Dr. Crane! Your glockenspiel has come to life!
Why not? Some models of superstring theory operate in 26 dimensions. If 3D’ers can postulate 26 dimensions and consider the existence thereof as real, I doubt that the postulation of one additional dimension to a 2D’er should be much of a stretch.