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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
DOI: https://doi.org/10.1090/S0002-9939-06-08489-9
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.


References [Enhancements On Off] (What's this?)

  • 1. N. Honda, Equivariant deformations of meromorphic actions on compact complex manifolds, Math. Ann. 319 (2001), 469-481. MR 1819878 (2002e:32019)
  • 2. N. Honda, Self-dual metrics and twenty-eight bitangents, J. Diff. Geom., to appear.
  • 3. D. Joyce, Explicit construction of self-dual 4-manifolds, Duke Math. J. 77 (1995), 519-552. MR 1324633 (96d:53049)
  • 4. C. LeBrun, Explicit self-dual metrics on $ {\mathbf{CP}}^2\char93 \cdots\char93 {\mathbf{CP}}^2$, J. Diff. Geom. 34 (1991), 223-253. MR 1114461 (92g:53040)
  • 5. C. LeBrun, Self-dual manifolds and hyperbolic geometry, Einstein metrics and Yang-Mills connections (Sanda, 1990), Lecture Notes in Pure and Appl. Math. 145 (1993), 99-131. MR 1215284 (94h:53060)
  • 6. C. LeBrun, Twistors, Kähler manifolds and bimeromorphic geometry. I, J. Amer. Math.Soc. 5 (1992), 289-316. MR 1137098 (92m:32052)
  • 7. H. Pedersen, Y. S. Poon, Equivariant connected sums of compact self-dual manifolds, Math. Ann. 301 (1995), 717-749. MR 1326765 (95m:53069)
  • 8. Y. S. Poon, Compact self-dual manifolds of positive scalar curvature, J. Diff. Geom. 24 (1986), 97-132. MR 0857378 (88b:32022)

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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

DOI: https://doi.org/10.1090/S0002-9939-06-08489-9
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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