A Construction of Einstein-Weyl Spaces via LeBrun-Mason Type Twistor Correspondence

摘要

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. Communicated by G.W. Gibbons