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Equivariant deformations of LeBrun's self-dual metrics with torus action

Author: Nobuhiro Honda
Journal: Proc. Amer. Math. Soc. 135 (2007), 495-505
MSC (2000): Primary 53C25
Published electronically: August 10, 2006
MathSciNet review: 2255296
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Abstract: We investigate $ U(1)$-equivariant deformations of C. LeBrun's self-dual metric with torus action. We explicitly determine all $ U(1)$-subgroups of the torus for which one can obtain $ U(1)$-equivariant deformations that do not preserve the whole of the torus action. This gives many new self-dual metrics with $ U(1)$-action which are not conformally isometric to LeBrun metrics. We also count the dimension of the moduli space of self-dual metrics with $ U(1)$-action obtained in this way.

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Nobuhiro Honda
Affiliation: Department of Mathematics, Graduate School of Science and Engineering, Tokyo Institute of Technology, 2-12-1, O-okayama, Meguro, 152-8551, Japan

Keywords: Self-dual metric, twistor space
Received by editor(s): April 28, 2005
Received by editor(s) in revised form: September 7, 2005
Published electronically: August 10, 2006
Additional Notes: This work was partially supported by Research Fellowships of the Japan Society for the Promotion of Science for Young Scientists.
Communicated by: Jon G. Wolfson
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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