About: Projective connection

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In differential geometry, a projective connection is a type of Cartan connection on a differentiable manifold. The structure of a projective connection is modeled on the geometry of projective space, rather than the affine space corresponding to an affine connection. Much like affine connections, projective connections also define geodesics. However, these geodesics are not affinely parametrized. Rather they are projectively parametrized, meaning that their preferred class of parameterizations is acted upon by the group of fractional linear transformations.

Attributes	Values
rdf:type	Thing road
rdfs:label	Projektive Mannigfaltigkeit (de) Projective connection (en)
rdfs:comment	In der Mathematik lassen sich projektive Mannigfaltigkeiten lokal durch projektive Koordinaten beschreiben. Zu den projektiven Mannigfaltigkeiten gehören unter anderem flache Mannigfaltigkeiten und hyperbolische Mannigfaltigkeiten und zahlreiche weitere in Differentialgeometrie und Topologie vorkommende Beispiele. (de) In differential geometry, a projective connection is a type of Cartan connection on a differentiable manifold. The structure of a projective connection is modeled on the geometry of projective space, rather than the affine space corresponding to an affine connection. Much like affine connections, projective connections also define geodesics. However, these geodesics are not affinely parametrized. Rather they are projectively parametrized, meaning that their preferred class of parameterizations is acted upon by the group of fractional linear transformations. (en)
dcterms:subject	Differential geometry Connection (mathematics)
Wikipage page ID	5776733 (xsd:integer)
Wikipage revision ID	1117700783 (xsd:integer)
Link from a Wikipage to another Wikipage	Projective frame Projective space Trace-free Homogeneous space Differential geometry Einstein notation Geodesics Lie algebra Affine connection Affine space Frame of reference Connection (mathematics) Homogeneous coordinates Differentiable manifold Differential geometry Cartan connection Solder form Affine parameter Maurer-Cartan form Basis of a vector space Fractional linear transformation Cartan geometry Reduction of structure group Isotropy group
Link from a Wikipage to an external page	http://www.numdam.org/item%3Fid=ASENS_1923_3_40__325_0 http://www.numdam.org/item%3Fid=BSMF_1924__52__205_0
sameAs	Projective connection Projective connection Projective connection Projective connection Projective connection Projective connection
dbp:wikiPageUsesTemplate	dbt:Springer dbt:Authority_control dbt:Citation dbt:Cite_book dbt:Cite_journal dbt:Refbegin dbt:Refend dbt:Reflist
author	Ü. Lumiste (en)
authorlink	Ülo Lumiste (en)
id	p/p075180 (en)
title	Projective connection (en)
has abstract	In der Mathematik lassen sich projektive Mannigfaltigkeiten lokal durch projektive Koordinaten beschreiben. Zu den projektiven Mannigfaltigkeiten gehören unter anderem flache Mannigfaltigkeiten und hyperbolische Mannigfaltigkeiten und zahlreiche weitere in Differentialgeometrie und Topologie vorkommende Beispiele. (de) In differential geometry, a projective connection is a type of Cartan connection on a differentiable manifold. The structure of a projective connection is modeled on the geometry of projective space, rather than the affine space corresponding to an affine connection. Much like affine connections, projective connections also define geodesics. However, these geodesics are not affinely parametrized. Rather they are projectively parametrized, meaning that their preferred class of parameterizations is acted upon by the group of fractional linear transformations. Like an affine connection, projective connections have associated torsion and curvature. (en)
gold:hypernym	Connection
prov:wasDerivedFrom	wikipedia-en:Projective_connection?oldid=1117700783&ns=0
page length (characters) of wiki page	8205 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Projective_connection
is Link from a Wikipage to another Wikipage of	List of differential geometry topics Connection (mathematics) Tractor bundle Geodesic Cross-ratio Affine connection Kobayashi metric Projective Projective differential geometry Torsion tensor Cartan connection Parabolic geometry (differential geometry) Complex projective structure
is Wikipage redirect of	Complex projective structure
is Wikipage disambiguates of	Projective
is foaf:primaryTopic of	wikipedia-en:Projective_connection

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