Conformal symmetries of self-dual hyperbolic monopole metrics

Details Conformal symmetries of self-dual hyperbolic monopole metrics Conformal symmetries of self-dual hyperbolic monopole metrics

2009-02-12

arxiv.org/abs/0902.2019v1

Mathematics

Differential Geometry

46 pages, 2 figures

Scientific paper

We determine the group of conformal automorphisms of the self-dual metrics on n#CP^2 due to LeBrun for n>2, 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>2 connected sums, 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 is a semi-direct product (U(1) \times U(1)) \times D_4, the dihedral group of order 8.

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