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Moduli of self-dual metrics on complex hyperbolic manifolds

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Abstract

On compact complex hyperbolic manifolds of complex dimension two,we show that the dimension of the space of infinitesimaldeformations of self-dual conformal structures is smallerthan that of the deformation obstruction space and thatevery self-dual metric with covariantly constant Ricci tensormust be a standard one upto rescalings and diffeomorphisms.

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