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March 2013 Conformal symmetries of self-dual hyperbolic monopole metrics
Nobuhiro Honda, Jeff Viaclovsky
Osaka J. Math. 50(1): 197-249 (March 2013).

Abstract

We determine the group of conformal automorphisms of the self-dual metrics on $n \# \mathbb{CP}^{2}$ due to LeBrun for $n \geq 3$, and Poon for $n = 2$. These metrics arise from an ansatz involving a circle bundle over hyperbolic three-space $\mathcal{H}^{3}$ minus a finite number of points, called monopole points. We show that for $n \geq 3$, any conformal automorphism is a lift of an isometry of $\mathcal{H}^{3}$ 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 $(\mathrm{U}(1) \times \mathrm{U}(1)) \rtimes \mathrm{D}_{4}$, where $\mathrm{D}_{4}$ is the dihedral group of order $8$.

Citation

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Nobuhiro Honda. Jeff Viaclovsky. "Conformal symmetries of self-dual hyperbolic monopole metrics." Osaka J. Math. 50 (1) 197 - 249, March 2013.

Information

Published: March 2013
First available in Project Euclid: 27 March 2013

zbMATH: 1276.53029
MathSciNet: MR3080638

Subjects:
Primary: 53A30
Secondary: 53C28

Rights: Copyright © 2013 Osaka University and Osaka City University, Departments of Mathematics

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Vol.50 • No. 1 • March 2013
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