Self-dual Einstein ACH metrics and CR GJMS operators in dimension three
Differential Geometry
2019-11-06 v3 Complex Variables
Abstract
By refining Matsumoto's construction of Einstein ACH metrics, we construct a one parameter family of ACH metrics which solve the Einstein equation to infinite order and have a given three dimensional CR structure at infinity. When the parameter is 0, the metric is self-dual to infinite order. As an application, we give another proof of the fact that three dimensional CR manifolds admit CR invariant powers of the sublaplacian (CR GJMS operators) of all orders, which has been proved by Gover-Graham. We also prove the convergence of the formal solutions when the CR structure is real analytic.
Cite
@article{arxiv.1802.01264,
title = {Self-dual Einstein ACH metrics and CR GJMS operators in dimension three},
author = {Taiji Marugame},
journal= {arXiv preprint arXiv:1802.01264},
year = {2019}
}
Comments
Final version; 22 pages; minor corrections, small change in the title