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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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Holomorphic Gauss normal map

Let $S$ be the embedded surface (assumed compact and not homeomorphic to a sphere) and let $S_1$ and $S_2$ be the subsets of $S$ where the Gaussian curvature is positive and negative, respectively. By …
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