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- Almost_flat_manifold abstract "In mathematics, a smooth compact manifold M is called almost flat if for any there is a Riemannian metric on M such that and is -flat, i.e. for the sectional curvature of we have .In fact, given n, there is a positive number such that if a n-dimensional manifold admits an -flat metric with diameter then it is almost flat. On the other hand one can fix the bound of sectional curvature and get the diameter going to zero, so the almost flat manifold is a special case of a collapsing manifold, which is collapsing along all directions.According to the Gromov—Ruh theorem, M is almost flat if and only if it is infranil. In particular, it is a finite factor of a nilmanifold, which is the total space of a principal torus bundle over a principal torus bundle over a torus.".
- Almost_flat_manifold wikiPageExternalLink 1214434488.
- Almost_flat_manifold wikiPageExternalLink 1214436698.
- Almost_flat_manifold wikiPageID "933946".
- Almost_flat_manifold wikiPageRevisionID "511595916".
- Almost_flat_manifold hasPhotoCollection Almost_flat_manifold.
- Almost_flat_manifold subject Category:Manifolds.
- Almost_flat_manifold subject Category:Riemannian_geometry.
- Almost_flat_manifold type Artifact100021939.
- Almost_flat_manifold type Conduit103089014.
- Almost_flat_manifold type Manifold103717750.
- Almost_flat_manifold type Manifolds.
- Almost_flat_manifold type Object100002684.
- Almost_flat_manifold type Passage103895293.
- Almost_flat_manifold type PhysicalEntity100001930.
- Almost_flat_manifold type Pipe103944672.
- Almost_flat_manifold type Tube104493505.
- Almost_flat_manifold type Way104564698.
- Almost_flat_manifold type Whole100003553.
- Almost_flat_manifold type YagoGeoEntity.
- Almost_flat_manifold type YagoPermanentlyLocatedEntity.
- Almost_flat_manifold comment "In mathematics, a smooth compact manifold M is called almost flat if for any there is a Riemannian metric on M such that and is -flat, i.e. for the sectional curvature of we have .In fact, given n, there is a positive number such that if a n-dimensional manifold admits an -flat metric with diameter then it is almost flat.".
- Almost_flat_manifold label "Almost flat manifold".
- Almost_flat_manifold sameAs m.03rbmw.
- Almost_flat_manifold sameAs Q4734002.
- Almost_flat_manifold sameAs Q4734002.
- Almost_flat_manifold sameAs Almost_flat_manifold.
- Almost_flat_manifold wasDerivedFrom Almost_flat_manifold?oldid=511595916.
- Almost_flat_manifold isPrimaryTopicOf Almost_flat_manifold.