Matches in DBpedia 2014 for { <http://dbpedia.org/resource/Affine_manifold> ?p ?o. }
Showing items 1 to 32 of
32
with 100 items per page.
- Affine_manifold abstract "In differential geometry, an affine manifold is a differentiable manifold equipped with a flat, torsion-free connection. Equivalently, it is a manifold that is (if connected) covered by an open subset of , with monodromy acting by affine transformations. This equivalence is an easy corollary of Cartan–Ambrose–Hicks theorem. Equivalently, it is a manifold equipped with an atlas—called the affine structure—with all transition functions between charts affine (that is, have constant jacobian matrix); two atlases are equivalent if the manifold admits an atlas subjugated to both, with transitions from both atlases to a smaller atlas being affine. A manifold having a distinguished affine structure is called an affine manifold and the charts which are affinely related to those of the affine structure are called affine charts. In each affine coordinate domain the coordinate vector fields form a parallelization of that domain, so there is an associated connection on each domain. These locally defined connections are the same on overlapping parts, so there is a unique connection associated with an affine structure. Note there is a link between linear connection (also called affine connection) and a web.".
- Affine_manifold wikiPageID "9996788".
- Affine_manifold wikiPageRevisionID "573748970".
- Affine_manifold hasPhotoCollection Affine_manifold.
- Affine_manifold subject Category:Affine_geometry.
- Affine_manifold subject Category:Differential_geometry.
- Affine_manifold subject Category:Group_theory.
- Affine_manifold subject Category:Manifolds.
- Affine_manifold subject Category:Structures_on_manifolds.
- Affine_manifold type Artifact100021939.
- Affine_manifold type Conduit103089014.
- Affine_manifold type Manifold103717750.
- Affine_manifold type Manifolds.
- Affine_manifold type Object100002684.
- Affine_manifold type Passage103895293.
- Affine_manifold type PhysicalEntity100001930.
- Affine_manifold type Pipe103944672.
- Affine_manifold type Structure104341686.
- Affine_manifold type StructuresOnManifolds.
- Affine_manifold type Tube104493505.
- Affine_manifold type Way104564698.
- Affine_manifold type Whole100003553.
- Affine_manifold type YagoGeoEntity.
- Affine_manifold type YagoPermanentlyLocatedEntity.
- Affine_manifold comment "In differential geometry, an affine manifold is a differentiable manifold equipped with a flat, torsion-free connection. Equivalently, it is a manifold that is (if connected) covered by an open subset of , with monodromy acting by affine transformations. This equivalence is an easy corollary of Cartan–Ambrose–Hicks theorem.".
- Affine_manifold label "Affine manifold".
- Affine_manifold sameAs m.02pz8qc.
- Affine_manifold sameAs Q4688942.
- Affine_manifold sameAs Q4688942.
- Affine_manifold sameAs Affine_manifold.
- Affine_manifold wasDerivedFrom Affine_manifold?oldid=573748970.
- Affine_manifold isPrimaryTopicOf Affine_manifold.