Volume 17, issue 5 (2013)

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Toric LeBrun metrics and Joyce metrics

Nobuhiro Honda and Jeff Viaclovsky

Geometry & Topology 17 (2013) 2923–2934
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.

Keywords
toric self-dual metrics
Mathematical Subject Classification 2010
Primary: 53A30
References
Publication
Received: 9 August 2012
Accepted: 31 May 2013
Published: 16 October 2013
Proposed: Simon Donaldson
Seconded: Tobias H Colding, Yasha Eliashberg
Authors
Nobuhiro Honda
Mathematical Institute
Tohoku University
Sendai, Miyagi, 980-8578
Japan
Jeff Viaclovsky
Department of Mathematics
University of Wisconsin
Madison, WI 53706
United States
http://www.math.wisc.edu/~jeffv/