Wave equations and the LeBrun-Mason correspondence
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- by Fuminori Nakata PDF
- Trans. Amer. Math. Soc. 364 (2012), 4763-4800 Request permission
Abstract:
The LeBrun-Mason twistor correspondences for $S^1$-invariant self-dual Zollfrei metrics are explicitly established. The correspondence is described by using explicit formulas for solutions of the wave equation and the monopole equation on the de Sitter three-space, and these formulas are explicitly given by using Radon-type integral transforms. We also obtain a critical condition for the LeBrun-Mason twistor spaces, and show that the twistor correspondence does not work well for twistor spaces which do not satisfy this condition.References
Additional Information
- Fuminori Nakata
- Affiliation: Department of Mathematics, Graduate School of Science and Engineering, Tokyo Institute of Technology, 2-12-1, O-okayama, Meguro, 152-8551, Japan
- Address at time of publication: Faculty of Human Development and Culture, Fukushima University, 1, Kanayagawa, Fukushima, 960-1296, Japan
- Email: nakata@math.titech.ac.jp, fnakata@educ.fukushima-u.ac.jp
- Received by editor(s): January 13, 2010
- Received by editor(s) in revised form: October 21, 2010
- Published electronically: April 18, 2012
- Additional Notes: This work is partially supported by Research Fellowships of the Japan Society for the Promotion of Science of Young Scientists
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 364 (2012), 4763-4800
- MSC (2010): Primary 53C28, 35L05, 53C50
- DOI: https://doi.org/10.1090/S0002-9947-2012-05509-7
- MathSciNet review: 2922609