- thanks for informing me about this concept. Translation surfaces can have genus > 0, while currently I'm only looking at flat Riemannian metrics with cone points on a genus-0 surface - a 2-sphere. People also study flat Riemannian metrics with cone points on higher genus surfaces.
More conceptually, translatiion surfaces are a practical way of describing Riemann surfaces equipped with a holomorphic 1-form (which comes from dz in the complex plane). Convex polyhedra are a practical way of describing flat Riemannian metrics with cone points on a 2-sphere. So the structures they describe are rather different.
John Carlos Baez
npub1nf…3nqe4
2026-06-12 07:26:47 UTC
in reply to nevent1q…g0wz
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2026-06-12 07:26:47 UTCEvent JSON
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