Zoll Metrics, Branched Covers, and Holomorphic Disks

الأصل · EN

We strengthen our previous results regarding the moduli spaces of Zoll metrics and Zoll projective structures on S². In particular, we describe a concrete, open condition which suffices to guarantee that a totally real embedding of RP² in CP₂ arises from a unique Zoll projective structure on the 2-sphere. Our methods ultimately reflect the special role such structures play in the initial value problem for the 3-dimensional Lorentzian Einstein-Weyl equations.