Equivariant deformations of LeBrun’s self-dual metrics with torus action
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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.References
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Additional Information
- 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
- Email: honda@math.titech.ac.jp
- 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
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 135 (2007), 495-505
- MSC (2000): Primary 53C25
- DOI: https://doi.org/10.1090/S0002-9939-06-08489-9
- MathSciNet review: 2255296