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Equivariant deformations of LeBrun's self-dual metrics with torus action
Author(s):
Nobuhiro
Honda
Journal:
Proc. Amer. Math. Soc.
135
(2007),
495-505.
MSC (2000):
Primary 53C25
Posted:
August 10, 2006
MathSciNet review:
2255296
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Abstract:
We investigate  -equivariant deformations of C. LeBrun's self-dual metric with torus action. We explicitly determine all  -subgroups of the torus for which one can obtain  -equivariant deformations that do not preserve the whole of the torus action. This gives many new self-dual metrics with  -action which are not conformally isometric to LeBrun metrics. We also count the dimension of the moduli space of self-dual metrics with  -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
DOI:
10.1090/S0002-9939-06-08489-9
PII:
S 0002-9939(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
Posted:
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 of article:
Copyright
2006,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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