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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.

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  • Projektive Mannigfaltigkeit
  • Projective connection
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  • 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.
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  • Ü. Lumiste
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  • p/p075180
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  • Projective connection
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  • 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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