# Question on topic for Mathoverflow?

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.

• Not really my area, but I'd hope (and sort of suspect) this type of question would be okay. "Research level" is a vague and crappy description, largely to keep out interlopers who are not serious or not in the business of mathematics. "Competent" from the standpoint of people at or above PhD students grappling with questions that arise in the path of serious study is more like it. (People taking overly seriously "research level", like "cutting edge", may be a problem here.) I'd say: give it a go. – Todd Trimble Nov 25 '20 at 2:37
• I see this question on Mathematics: 3-dimensional slice of $\zeta^{2,2}$ - but it is less that 24 hours old. So maybe you meant a different question when you said that it was "asked months ago"? – Martin Sleziak Nov 25 '20 at 7:58
• @MartinSleziak I was referencing this question mathoverflow.net/questions/368647/… – Jack Zimmerman Nov 25 '20 at 13:27
• I see. I misunderstood what you meant - I thought that you're talking about this question (i.e., the one mentioned in this post) but post on Mathematics. – Martin Sleziak Nov 25 '20 at 13:40
• I'd suggest to wait a little (say 48h) before cross-posting to MO. Or, since there's no feedback at all at MathSE, you could delete it there, and post a copy at MO. In case of a crosspost, mention the other post at each site. – YCor Nov 26 '20 at 11:09
• While it's not my area, the formulation "How could you define ..." seems perhaps a little vague to me(?) – Stefan Kohl Nov 26 '20 at 16:33
• The question as stated is ill-posed: You should explain what you mean by a "slice" in a semi-Riemannian manifold and what kind of a codimension 1 foliation you are looking for: Every 3-manifold admits a codimension 1 smooth foliation. – Moishe Kohan Dec 4 '20 at 21:43
• @MoisheKohan is this better? math.stackexchange.com/questions/3938818/… – Jack Zimmerman Dec 10 '20 at 16:27