CANONICAL ALMOST COMPLEX STRUCTURES ON ACH EINSTEIN MANIFOLDS

On asymptotically complex hyperbolic (ACH) Einstein manifolds, we consider a certain variational problem for almost complex structures compatible with the metric, for which the linearized Euler-Lagrange equation at Kaliler-Einstein structures is given by the Dolbeault Laplacian acting on (0, 1)-forms with values in the holomorphic tangent bundle. A deformation result of Einstein ACH metrics associated with critical almost complex structures for this variational problem is given. It is also shown that the asymptotic expansion of a critical almost complex structure is determined by the induced (possibly nonintegrable) CR structure on the boundary at infinity up to a certain order.