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Riemann surface

In mathematics, particularly in complex analysis, a Riemann surface is a connected one-dimensional complex manifold. These surfaces were first studied by and are named after Bernhard Riemann. Riemann surfaces can be thought of as deformed versions of the complex plane: locally near every point they look like patches of the complex plane, but the global…

Art, Classification of Riemann surfaces & Definitions

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Classification of Riemann surfaces

20 related topics

Definitions

17 related topics

Further definitions and properties

16 related topics

Isometries of Riemann surfaces

12 related topics

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Overview

Definitions

Examples

Further definitions and properties

Analytic vs. algebraic

Classification of Riemann surfaces

Maps between Riemann surfaces

Isometries of Riemann surfaces

Theorems regarding Riemann surfaces

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Riemann surface

Nodes126
Edges125
Triples130
Avg. degree1.98
Density0.015873
Components1

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Riemann surface

Top relations

related to Examples · 12
Riemann surface → As, CP, Every, Important, It, More, On, Riemann, The, The Riemann, These, This
related to Functions · 11
Riemann surface → Abel, Every, However, In, Jacobi, Meromorphic, More, Riemann, Siegel, Stein, This
related to Analytic vs. algebraic · 10
Riemann surface → Actually, As, Chow's, If, On, Riemann, The, The Weierstrass, There, This
related to External links · 10
Riemann surface → Complex Analysis, EMS Press, Encyclopedia, Harvard Math, Harvard University, Mathematics, McMullen, PDF, Riemann, Riemann Surfaces Math
related to Classification of Riemann surfaces · 9
Riemann surface → Geometrically, In, Koebe, Poincaré, Riemann, Riemannian, That, The, This
related to Definitions · 9
Riemann surface → Again, Choosing, Hausdorff, Riemann, Riemannian, The, There, This, Two
related to Isometries of Riemann surfaces · 9
Riemann surface → Abelian, For, Hurwitz, Hurwitz's, In, It, Möbius, Riemann, The
related to Algebraic curves · 7
Riemann surface → Every, If, Likewise, Riemann, This, Weierstrass, When
related to Hyperbolic Riemann surfaces · 7
Riemann surface → Fuchsian, However, In, Its Teichmüller, Riemann, The, Then
is a · 6
Riemann surface → complex algebraic curve by Chow's theorem and the Riemann, connected one-dimensional complex manifold, projective variety, Riemann surface.The 2-sphere S 2, Stein manifold.In contrast, surface

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Important terminology

riemann surface displaystyle complex surfaces mathbb sphere every genus group plane holomorphic two manifold algebraic one structure real function functions

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Riemann surfaceis aconnected one-dimensional complex manifold0.90text
Riemann surfaceis asurface0.90text
Riemann surfaceis acomplex algebraic curve by Chow's theorem and the Riemann0.90text
Riemann surfaceis aRiemann surface.The 2-sphere S 20.90text
Riemann surfaceis aStein manifold.In contrast0.90text
Riemann surfaceis aprojective variety0.90text
Riemann surfacerelated to Algebraic curvesIf0.60section
Riemann surfacerelated to Algebraic curvesRiemann0.60section
Riemann surfacerelated to Algebraic curvesThis0.60section
Riemann surfacerelated to Algebraic curvesEvery0.60section
Riemann surfacerelated to Algebraic curvesWeierstrass0.60section
Riemann surfacerelated to Algebraic curvesLikewise0.60section

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