2 problems

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Existence of non-C^1-conformal spacelike Zoll metrics with a Killing field
Non-conformality conjecture. There exist spacelike Zoll metrics with a Killing field which are not $C^1$ -conformal to a cover of de Sitter.
Conjectureopenconformal-geometry lorentzian-geometry zoll-surfacesarXiv posted 2 days ago
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Tameness conjecture for the rolling-surface $G_2/P_2$ -geometry
Let $S$ and $S'$ be Riemannian surfaces whose Gauss curvatures differ at every pair of points, and let $M$ be the space of linear isometries between tangent planes of $S$ and $S'$ .…
Conjectureopencartan-geometries g2-geometries zoll-surfacesarXiv posted 2 days ago

Existence of non-C^1-conformal spacelike Zoll metrics with a Killing field