My question, asked months ago, was well received. Now...

I'm wondering if this question is on-topic for MathOverflow:

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 $\zeta^{2,2}$? Does there exist a construction of a foliation of this 3-dimensional slice, using leaves of dimension 2?

Is it research level? How close to research level is it?

Thanks so much.