# 3-dimensional slice of $\zeta^{2,2}$

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.