Consider a semi-Riemannian manifold $\zeta^{2,2}$ with metric, $g=\frac{dxdy}{xy}+\frac{dudv}{v-uv}.$
How could you define a 3-dimensional slice of $\zeta^{2,2}$? What would it look like?
I guess one possibility is using 2 dimensions of space and 1 dimension of time, and another possibility is 2 dimensions of time and 1 dimension of space.