$\{x_1,\ldots,x_n,\xi_{m+1},\ldots,\xi_n\in\mathbb{R},\xi_1=\ldots=\xi_m=0\}$ is a "model" codimension $m$ coisotropic submanifold of $T^*\mathbb{R}^n$, and is of course noncompact. Is there such a thing as a "model" compact coisotropic?
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$\begingroup$ Consider $\mathbb C P ^n $ with its standard (Kaehler) symplectic structure and homogeneous coordinates $[z_0:\cdots:z_n]$. The submanifolds defined by $\Im z_j=0$ for $j=0,\ldots,m$ and $0\leq m\leq n$ are compact and coisotropic (the case $m=n$ is Lagrangian and gives $\mathbb R P ^n$). $\endgroup$– Claudio GorodskiCommented Apr 12, 2014 at 13:58
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There are well-known normal form theorems for all kind of constant rank submanifolds in symplectic manifolds, even global statements (and only such a thing seems to be of interest if you want to talk about compactness). You find these statements at many places, I personally like very much the discussion in Eckhard Meinrenken's lecture notes on symplectic geometry, available on his homepage.
answered Feb 11, 2014 at 9:20