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- 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.jpg?width=300.
- Riemann_surface wikiPageExternalLink dieideederrieman00weyluoft.
- Riemann_surface wikiPageExternalLink book.html.
- Riemann_surface wikiPageID "173181".
- Riemann_surface wikiPageRevisionID "600531732".
- Riemann_surface hasPhotoCollection Riemann_surface.
- Riemann_surface id "6297".
- Riemann_surface id "p/r082040".
- Riemann_surface title "Riemann Surface".
- Riemann_surface title "Riemann surface".
- Riemann_surface subject Category:Riemann_surfaces.
- Riemann_surface type Artifact100021939.
- Riemann_surface type Object100002684.
- Riemann_surface type PhysicalEntity100001930.
- Riemann_surface type RiemannSurfaces.
- Riemann_surface type Surface104362025.
- Riemann_surface type Whole100003553.
- Riemann_surface comment "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.".
- Riemann_surface label "Powierzchnia Riemanna".
- Riemann_surface label "Riemann surface".
- Riemann_surface label "Riemann-oppervlak".
- Riemann_surface label "Riemannsche Fläche".
- Riemann_surface label "Superficie de Riemann".
- Riemann_surface label "Superficie di Riemann".
- Riemann_surface label "Superfície de Riemann".
- Riemann_surface label "Surface de Riemann".
- Riemann_surface label "Риманова поверхность".
- Riemann_surface label "سطح ريمان".
- Riemann_surface label "リーマン面".
- Riemann_surface label "黎曼曲面".
- Riemann_surface sameAs Riemannsche_Fläche.
- Riemann_surface sameAs Επιφάνεια_Riemann.
- Riemann_surface sameAs Superficie_de_Riemann.
- Riemann_surface sameAs Surface_de_Riemann.
- Riemann_surface sameAs Superficie_di_Riemann.
- Riemann_surface sameAs リーマン面.
- Riemann_surface sameAs 리만_곡면.
- Riemann_surface sameAs Riemann-oppervlak.
- Riemann_surface sameAs Powierzchnia_Riemanna.
- Riemann_surface sameAs Superfície_de_Riemann.
- Riemann_surface sameAs m.017bp7.
- Riemann_surface sameAs Q753035.
- Riemann_surface sameAs Q753035.
- Riemann_surface sameAs Riemann_surface.
- Riemann_surface wasDerivedFrom Riemann_surface?oldid=600531732.
- Riemann_surface depiction Riemann_sqrt.jpg.
- Riemann_surface isPrimaryTopicOf Riemann_surface.