A Construction of Einstein-Weyl Spaces via LeBrun-Mason Type Twistor Correspondence |
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Authors: | Fuminori Nakata |
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Institution: | (1) Department of Mathematics, Graduate School of Science and Engineering, Tokyo Institute of Technology, 2-12-1, O-okayama, Meguro 152-8551, Japan |
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Abstract: | We construct infinitely many Einstein-Weyl structures on of signature (− + +) which is sufficiently close to the model case of constant curvature, and on which the space-like geodesics
are all closed. Such a structure is obtained as a parameter space of a family of holomorphic disks which is associated to
a small perturbation of the diagonal of . The geometry of constructed Einstein-Weyl spaces is well understood from the configuration of holomorphic disks. We also
review Einstein-Weyl structures and their properties in the former half of this article.
This work is partially supported by Grant-in-Aid for Scientific Research of the Japan Society for the Promotion of Science. |
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Keywords: | |
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