### Abstract

We determine the group of conformal automorphisms of the self-dual metrics on n#CP^{2} due to LeBrun for n≥3, and Poon for n=2. These metrics arise from an ansatz involving a circle bundle over hyperbolic three-space H^{3} minus a finite number of points, called monopole points. We show that for n≥3, any conformal automorphism is a lift of an isometry of H^{3} which preserves the set of monopole points. Furthermore, we prove that for n=2, such lifts form a subgroup of index 2 in the full automorphism group, which we show to be a semi-direct product (U(1)×U(1))×D_{4}, where D_{4} is the dihedral group of order 8.

Original language | English |
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Pages (from-to) | 197-249 |

Number of pages | 53 |

Journal | Osaka Journal of Mathematics |

Volume | 50 |

Issue number | 1 |

Publication status | Published - 2013 Mar 1 |

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Honda, N., & Viaclovsky, J. (2013). Conformal symmetries of self-dual hyperbolic monopole metrics.

*Osaka Journal of Mathematics*,*50*(1), 197-249.