Zoll Metrics, Branched Covers, and Holomorphic Disks

Details Zoll Metrics, Branched Covers, and Holomorphic Disks Zoll Metrics, Branched Covers, and Holomorphic Disks

2010-02-16

arxiv.org/abs/1002.2993v1

Mathematics

Differential Geometry

21 pages, LaTeX2e

Scientific paper

We strengthen our previous results regarding the moduli spaces of Zoll metrics and Zoll projective structures on S^2. In particular, we describe a concrete, open condition which suffices to guarantee that a totally real embedding of RP^2 in CP_2 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.

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