We determine the group of conformal automorphisms of the self-dual metrics on n#CP2 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 H3 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 H3 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))×D4, where D4 is the dihedral group of order 8.
|Number of pages||53|
|Journal||Osaka Journal of Mathematics|
|Publication status||Published - 2013 Mar 1|
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