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Can we foliate the anti-de sitter spacetime in 3 dimensions by hyperbolic Riemann surfaces? -- I think this is possible, but got stuck at finding the particular projective mapping that does this. Can someone please help me?

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    $\begingroup$ Not sure this is what you want, but if the anti-de Sitter spacetime in $3$ dimensions is the set $X$ of vectors of length $1$ in $\mathbf R^{2,2}$, then you have a well defined map $X\to S^1$ (take the first two coordinates and normalize) whose fiber over any vector is a two sheeted hyperboloïd. $\endgroup$
    – few_reps
    Commented Oct 14, 2015 at 11:21
  • $\begingroup$ (sorry, a sheet of a two-sheeted hyperboloïd). $\endgroup$
    – few_reps
    Commented Oct 14, 2015 at 11:33

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