  The recent example of Hanges: $P = \partial_t^2 + t^2\Delta_x +
\partial^2_{\theta(x)}$ in $R^3$ is analytic hypoelliptic in the sense of germs
but not in the strong sense in any neighborhood of the origin. And its
characteristic variety is non-symplectic. We give a purely $L^2,$ and hence
quite flexible, proof of this result and generalizations, and link it to, and
contrast it with, the celebrated Baouendi-Goulaouic operator. We point out that
the results are consistent with the conjecture of Treves.
