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.


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