| Abstract: |
| Let $M$ be a three dimensional strictly pseudoconvex CR manifold. By refining Matsumoto`s construction, we construct a one parameter family of ACH metrics
$g^\lambda_{IJ}\ (\lambda\in\mathbb{R})$ on $M\times[0, \infty)$,
which solve the Einstein equation to infinite order. When $\lambda=0$, the metric $g^0_{IJ}$ is
also self-dual to infinite order. As an application, we give another proof of the fact that a three dimensional CR manifold admits CR invariant powers of the sublaplacian of all orders, which has been shown by Gover--Graham. |
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