Riemann Uniformization Theorem

Theorem

Every connected $2$-dimensional manifold has a complete Riemannian metric with the constant Gaussian curvature.


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Proof


This theorem requires a proof.
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Source of Name

This entry was named for Georg Friedrich Bernhard Riemann.


Sources

  • 2018: John M. Lee: Introduction to Riemannian Manifolds (2nd ed.) ... (previous) ... (next): $\S 1$: What Is Curvature? Surfaces in Space
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