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Transactions of the American Mathematical Society

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Wave equations and the LeBrun-Mason correspondence

Author: Fuminori Nakata
Journal: Trans. Amer. Math. Soc. 364 (2012), 4763-4800
MSC (2010): Primary 53C28, 35L05, 53C50
Published electronically: April 18, 2012
MathSciNet review: 2922609
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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.

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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

Keywords: Twistor method, holomorphic disks, indefinite metric, wave equation, monopole equation, Radon transform
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
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.