Toric LeBrun metrics and Joyce metrics

Published 10 Aug 2012 in math.DG | (1208.2065v1)

Abstract: We show that, on the connected sum of complex projective planes, any toric LeBrun metric can be identified with a Joyce metric admitting a semi-free circle action through an explicit conformal equivalence. A crucial ingredient of the proof is an explicit connection form for toric LeBrun metrics.

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