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Riemann surfaces(Riemannian surfaces) is one dimensional complex manifold. For questions about classical examples in complex analysis, complex geometry, surface topology.
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Analytic curve on Riemann surface
Suppose there is a closed analytic curve $C$ on a Riemann surface $S$, that is the image of a map $\gamma$ from the equator $E$ of the Riemann sphere to the surface $S$ which is a restriction of a o …