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MODULI OF SELF-DUAL METRICS ON COMPLEX HYPERBOLIC MANIFOLDS

  • Published : 2002.02.01

Abstract

On compact complex hyperbolic manifolds of complex dimension two, we show that the dimension of the space of infinitesimal 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 diffeomorphisms.

Keywords

infinitesimal deformations;self-dual conformal structures;compact complex hyperbolic manifolds;deformation obstruction space;covariantly constant Ricci tensor

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Cited by

  1. Stability of complex hyperbolic space under curvature-normalized Ricci flow vol.164, pp.1, 2013, https://doi.org/10.1007/s10711-012-9770-9