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On compact complex hyperbolic manifolds of complex dimension two, we show that the dimension of the space of infinites- imal deformations of self-dual conformal structures is smaller than that of the deformation obstruction space and that every self-dual metric with covariantly constant Ricci tensor must be a standard one upto rescalings and dieomorphisms.

MODULI OF SELF-DUAL METRICS ON COMPLEX HYPERBOLIC MANIFOLDS