About: Collapsing manifold

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In Riemannian geometry, a collapsing or collapsed manifold is an n-dimensional manifold M that admits a sequence of Riemannian metrics gi, such that as i goes to infinity the manifold is close to a k-dimensional space, where k < n, in the Gromov–Hausdorff distance sense. Generally there are some restrictions on the sectional curvatures of (M, gi). The simplest example is a flat manifold, whose metric can be rescaled by 1/i, so that the manifold is close to a point, but its curvature remains 0 for all i.

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rdf:type	place yago:WikicatManifolds yago:Artifact100021939 yago:Conduit103089014 yago:Manifold103717750 yago:Object100002684 yago:Passage103895293 yago:PhysicalEntity100001930 yago:Pipe103944672 yago:YagoGeoEntity yago:YagoPermanentlyLocatedEntity yago:Tube104493505 yago:Way104564698 yago:Whole100003553
rdfs:label	Collapsing manifold (en) Коллапс (геометрия) (ru)
rdfs:comment	In Riemannian geometry, a collapsing or collapsed manifold is an n-dimensional manifold M that admits a sequence of Riemannian metrics gi, such that as i goes to infinity the manifold is close to a k-dimensional space, where k < n, in the Gromov–Hausdorff distance sense. Generally there are some restrictions on the sectional curvatures of (M, gi). The simplest example is a flat manifold, whose metric can be rescaled by 1/i, so that the manifold is close to a point, but its curvature remains 0 for all i. (en) Коллапс — тип последовательности пространств, обычно римановых многообразий, которая существенно меняет локальную структуру (в частности теряет размерность) при переходе к пределу. (ru)
dcterms:subject	Manifolds Riemannian geometry
Wikipage page ID	16838918 (xsd:integer)
Wikipage revision ID	860322478 (xsd:integer)
Link from a Wikipage to another Wikipage	Alexandrov space Manifolds Kenji Fukaya Riemannian geometry Riemannian manifold Jeff Cheeger Nilmanifold Riemannian geometry Gromov–Hausdorff convergence Flat manifold Injectivity radius Sectional curvature Manifold (mathematics) Mikhail Gromov (mathematician) dbr:Almost_nonnegatively_curved_manifold dbr:F-structure dbr:N-structure
sameAs	Collapsing manifold Collapsing manifold Collapsing manifold Collapsing manifold Collapsing manifold
dbp:wikiPageUsesTemplate	dbt:Fact dbt:For dbt:Unreferenced
has abstract	In Riemannian geometry, a collapsing or collapsed manifold is an n-dimensional manifold M that admits a sequence of Riemannian metrics gi, such that as i goes to infinity the manifold is close to a k-dimensional space, where k < n, in the Gromov–Hausdorff distance sense. Generally there are some restrictions on the sectional curvatures of (M, gi). The simplest example is a flat manifold, whose metric can be rescaled by 1/i, so that the manifold is close to a point, but its curvature remains 0 for all i. (en) Коллапс — тип последовательности пространств, обычно римановых многообразий, которая существенно меняет локальную структуру (в частности теряет размерность) при переходе к пределу. (ru)
gold:hypernym	M
prov:wasDerivedFrom	wikipedia-en:Collapsing_manifold?oldid=860322478&ns=0
page length (characters) of wiki page	3772 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Collapsing_manifold
is Link from a Wikipage to another Wikipage of	Almost flat manifold Berger's sphere Collapse Collapsing Manifold Glossary of Riemannian and metric geometry Grigori Perelman Jeff Cheeger Mikhael Gromov (mathematician) Minimal volume Collapse (geometry)
is Wikipage redirect of	Collapsing Manifold Collapse (geometry)
is foaf:primaryTopic of	wikipedia-en:Collapsing_manifold

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