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Statements

Subject Item
dbr:Projective_connection
rdf:type
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Projektive Mannigfaltigkeit Projective connection
rdfs:comment
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. 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.
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dbr:Homogeneous_space dbr:Affine_connection dbr:Group_action dbr:Differentiable_manifold dbc:Connection_(mathematics) dbr:Geodesic dbr:Affine_space dbr:Projective_frame dbr:Maurer–Cartan_form dbr:Differential_geometry dbr:Lie_algebra dbr:Basis_(linear_algebra) dbr:G-structure_on_a_manifold dbc:Differential_geometry dbr:Frame_of_reference dbr:Projective_space dbr:Linear_fractional_transformation dbr:Trace_(linear_algebra) dbr:Cartan_connection dbr:Homogeneous_coordinates dbr:Solder_form
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dbp:author
Ü. Lumiste
dbp:id
p/p075180
dbp:title
Projective connection
dbo: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. 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.
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