Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Riemann_surface> ?p ?o }
- Riemann_surface abstract "In mathematics, particularly in complex analysis, a Riemann surface, first studied by and named after Bernhard Riemann, is a one-dimensional complex manifold. 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 topology can be quite different. For example, they can look like a sphere or a torus or several sheets glued together.The main point of Riemann surfaces is that holomorphic functions may be defined between them. Riemann surfaces are nowadays considered the natural setting for studying the global behavior of these functions, especially multi-valued functions such as the square root and other algebraic functions, or the logarithm.Every Riemann surface is a two-dimensional real analytic manifold (i.e., a surface), but it contains more structure (specifically a complex structure) which is needed for the unambiguous definition of holomorphic functions. A two-dimensional real manifold can be turned into a Riemann surface (usually in several inequivalent ways) if and only if it is orientable and metrizable. So the sphere and torus admit complex structures, but the Möbius strip, Klein bottle and projective plane do not.Geometrical facts about Riemann surfaces are as "nice" as possible, and they often provide the intuition and motivation for generalizations to other curves, manifolds or varieties. The Riemann–Roch theorem is a prime example of this influence.".
- Riemann_surface thumbnail Riemann_sqrt.svg?width=300.
- Riemann_surface wikiPageExternalLink dieideederrieman00weyluoft.
- Riemann_surface wikiPageExternalLink book.html.
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- Riemann_surface wikiPageWikiLink Abelian_variety.
- Riemann_surface wikiPageWikiLink Algebraic_Geometry_(book).
- Riemann_surface wikiPageWikiLink Algebraic_curve.
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- Riemann_surface wikiPageWikiLink Algebraic_geometry.
- Riemann_surface wikiPageWikiLink Algebraic_geometry_and_analytic_geometry.
- Riemann_surface wikiPageWikiLink Algebraic_topology.
- Riemann_surface wikiPageWikiLink Analytic_continuation.
- Riemann_surface wikiPageWikiLink Analytic_geometry.
- Riemann_surface wikiPageWikiLink Angle.
- Riemann_surface wikiPageWikiLink Atlas_(topology).
- Riemann_surface wikiPageWikiLink Bernhard_Riemann.
- Riemann_surface wikiPageWikiLink Bijection.
- Riemann_surface wikiPageWikiLink Bijective.
- Riemann_surface wikiPageWikiLink Bolza_surface.
- Riemann_surface wikiPageWikiLink Branching_theorem.
- Riemann_surface wikiPageWikiLink Brings_surface.
- Riemann_surface wikiPageWikiLink Cantor_set.
- Riemann_surface wikiPageWikiLink Category:Riemann_surfaces.
- Riemann_surface wikiPageWikiLink Circumference.
- Riemann_surface wikiPageWikiLink Compact_space.
- Riemann_surface wikiPageWikiLink Complete_metric_space.
- Riemann_surface wikiPageWikiLink Completeness_(topology).
- Riemann_surface wikiPageWikiLink Complex_Manifold.
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- Riemann_surface wikiPageWikiLink Complex_conjugate.
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- Riemann_surface wikiPageWikiLink Complex_number.
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- Riemann_surface wikiPageWikiLink Complex_projective_line.
- Riemann_surface wikiPageWikiLink Complex_projective_space.
- Riemann_surface wikiPageWikiLink Conformal_equivalence.
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- Riemann_surface wikiPageWikiLink Conformally_equivalent.
- Riemann_surface wikiPageWikiLink Covering_space.
- Riemann_surface wikiPageWikiLink Curvature.
- Riemann_surface wikiPageWikiLink Deck_transformation.
- Riemann_surface wikiPageWikiLink Dessin_denfant.
- Riemann_surface wikiPageWikiLink Determinant.
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- Riemann_surface wikiPageWikiLink Disk_(mathematics).
- Riemann_surface wikiPageWikiLink Dover_Publications.
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- Riemann_surface wikiPageWikiLink Equivalence_class.
- Riemann_surface wikiPageWikiLink Euclidean_distance.
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- Riemann_surface wikiPageWikiLink Field_extension.
- Riemann_surface wikiPageWikiLink Free_regular_set.
- Riemann_surface wikiPageWikiLink Fuchsian_group.
- Riemann_surface wikiPageWikiLink Fuchsian_model.
- Riemann_surface wikiPageWikiLink Function_(mathematics).
- Riemann_surface wikiPageWikiLink Function_field_of_an_algebraic_variety.
- Riemann_surface wikiPageWikiLink Fundamental_domain.
- Riemann_surface wikiPageWikiLink Fundamental_polygon.
- Riemann_surface wikiPageWikiLink Gauss–Bonnet_theorem.
- Riemann_surface wikiPageWikiLink Generating_set.
- Riemann_surface wikiPageWikiLink Generator_(mathematics).
- Riemann_surface wikiPageWikiLink Genus_(mathematics).
- Riemann_surface wikiPageWikiLink Hausdorff_space.
- Riemann_surface wikiPageWikiLink Holomorphic_function.
- Riemann_surface wikiPageWikiLink Homeomorphic.
- Riemann_surface wikiPageWikiLink Homeomorphism.
- Riemann_surface wikiPageWikiLink Hurwitzs_automorphisms_theorem.
- Riemann_surface wikiPageWikiLink Hyperelliptic_surface.
- Riemann_surface wikiPageWikiLink Identity_theorem_for_Riemann_surfaces.
- Riemann_surface wikiPageWikiLink Imaginary_part.
- Riemann_surface wikiPageWikiLink Immersion_(mathematics).
- Riemann_surface wikiPageWikiLink J-invariant.
- Riemann_surface wikiPageWikiLink Jacobian_variety.
- Riemann_surface wikiPageWikiLink Klein_bottle.
- Riemann_surface wikiPageWikiLink Klein_quartic.
- Riemann_surface wikiPageWikiLink Kähler_manifold.
- Riemann_surface wikiPageWikiLink Lars_Ahlfors.
- Riemann_surface wikiPageWikiLink Lattice_(group).
- Riemann_surface wikiPageWikiLink Liouvilles_theorem_(complex_analysis).
- Riemann_surface wikiPageWikiLink Lipman_Bers.
- Riemann_surface wikiPageWikiLink Little_Picard_theorem.
- Riemann_surface wikiPageWikiLink Lorentz_surface.
- Riemann_surface wikiPageWikiLink Macbeath_surface.
- Riemann_surface wikiPageWikiLink Manifold.
- Riemann_surface wikiPageWikiLink Mapping_class_group.
- Riemann_surface wikiPageWikiLink Mathematics.
- Riemann_surface wikiPageWikiLink Maximum_principle.
- Riemann_surface wikiPageWikiLink Meromorphic.
- Riemann_surface wikiPageWikiLink Meromorphic_function.
- Riemann_surface wikiPageWikiLink Moduli_space.