About: Klein surface

Facets (new session)
Description
Metadata
Settings
- Rule:
- Inverse Functional Properties:
- "Same As":

About: Klein surface Goto Sponge NotDistinct Permalink

An Entity of Type : yago:WikicatSurfaces, within Data Space : dbpedia.org associated with source document(s)
QRcode icon

http://dbpedia.org/describe/?url=http%3A%2F%2Fdbpedia.org%2Fresource%2FKlein_surface

In mathematics, a Klein surface is a dianalytic manifold of complex dimension 1. Klein surfaces may have a boundary and need not be orientable. Klein surfaces generalize Riemann surfaces. While the latter are used to study algebraic curves over the complex numbers analytically, the former are used to study algebraic curves over the real numbers analytically. Klein surfaces were introduced by Felix Klein in 1882.

Attributes	Values
rdf:type	yago:Artifact100021939 yago:Object100002684 yago:PhysicalEntity100001930 yago:Surface104362025 yago:Whole100003553 yago:WikicatSurfaces
rdfs:label	Klein surface (en)
rdfs:comment	In mathematics, a Klein surface is a dianalytic manifold of complex dimension 1. Klein surfaces may have a boundary and need not be orientable. Klein surfaces generalize Riemann surfaces. While the latter are used to study algebraic curves over the complex numbers analytically, the former are used to study algebraic curves over the real numbers analytically. Klein surfaces were introduced by Felix Klein in 1882. (en)
dcterms:subject	Surfaces
Wikipage page ID	20478442 (xsd:integer)
Wikipage revision ID	1106859417 (xsd:integer)
Link from a Wikipage to another Wikipage	Algebraic function field Surfaces Homeomorphic Riemann surface Complex plane Connected component (topology) Genus (mathematics) Geodesic Möbius strip Equivalence of categories Annulus (mathematics) Surface (topology) Torus Algebraic curve Felix Klein Fixed point (mathematics) Dianalytic manifold Projective variety Involution (mathematics) Riemann sphere Riemann surfaces Homeomorphism Differentiable manifold Manifold Contravariant functor Glossary of scheme theory Klein bottle Category (mathematics) Orientable manifold Real projective plane Scheme (mathematics) Euler characteristic Smooth scheme Tangent vector Meromorphic Morphism of varieties Closed disk
sameAs	Klein surface Klein surface Klein surface Klein surface
dbp:wikiPageUsesTemplate	dbt:About dbt:Citation dbt:Reflist
has abstract	In mathematics, a Klein surface is a dianalytic manifold of complex dimension 1. Klein surfaces may have a boundary and need not be orientable. Klein surfaces generalize Riemann surfaces. While the latter are used to study algebraic curves over the complex numbers analytically, the former are used to study algebraic curves over the real numbers analytically. Klein surfaces were introduced by Felix Klein in 1882. A Klein surface is a surface (i.e., a differentiable manifold of real dimension 2) on which the notion of angle between two tangent vectors at a given point is well-defined, and so is the angle between two intersecting curves on the surface. These angles are in the range [0,π]; since the surface carries no notion of orientation, it is not possible to distinguish between the angles α and −α. (By contrast, on Riemann surfaces are oriented and angles in the range of (-π,π] can be meaningfully defined.) The length of curves, the area of submanifolds and the notion of geodesic are not defined on Klein surfaces. Two Klein surfaces X and Y are considered equivalent if there are conformal (i.e. angle-preserving but not necessarily orientation-preserving) differentiable maps f:X→Y and g:Y→X that map boundary to boundary and satisfy fg = idY and gf = idX. (en)
gold:hypernym	Manifold
prov:wasDerivedFrom	wikipedia-en:Klein_surface?oldid=1106859417&ns=0
page length (characters) of wiki page	7985 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Klein_surface
is Link from a Wikipage to another Wikipage of	Algebraic function field Dianalytic manifold List of things named after Felix Klein Klein Klein Surface
is Wikipage redirect of	Klein Surface
is Wikipage disambiguates of	Klein
is foaf:primaryTopic of	wikipedia-en:Klein_surface

Faceted Search & Find service v1.17_git139 as of Feb 29 2024

Alternative Linked Data Documents: ODE Content Formats:

RDF

ODATA

Microdata

About

OpenLink Virtuoso version 08.03.3330 as of Mar 19 2024, on Linux (x86_64-generic-linux-glibc212), Single-Server Edition (378 GB total memory, 62 GB memory in use)
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2024 OpenLink Software