Communications in Analysis and Geometry

Volume 18 (2010)

Number 3

Zoll metrics, branched covers, and holomorphic disks

Pages: 475 – 502



Claude LeBrun (Mathematics Department, State University of New York, Stony Brook)

L.J. Mason (Mathematical Institute, University of Oxford)


We strengthen our previous results \cite{lmzoll}regarding the moduli spaces of Zoll metrics and Zollprojective structures on $S^2$. In particular, we describea concrete, open condition which suffices to guaranteethat a totally real embedding $\RP^2\hookrightarrow \CP_2$arises from a unique Zoll projective structure on thetwo-sphere. Our methods ultimately reflect the special rolesuch structures play in the initial value problem for thethree-dimensional Lorentzian Einstein–Weyl equations.

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