About: Gromov's systolic inequality for essential manifolds

Facets (new session)
Description
Metadata
Settings
- Rule:
- Inverse Functional Properties:
- "Same As":

About: Gromov's systolic inequality for essential manifolds Goto Sponge NotDistinct Permalink

An Entity of Type : yago:WikicatGeometricInequalities, within Data Space : dbpedia.org associated with source document(s)
QRcode icon

http://dbpedia.org/describe/?url=http%3A%2F%2Fdbpedia.org%2Fresource%2FGromov%27s_systolic_inequality_for_essential_manifolds

In the mathematical field of Riemannian geometry, M. Gromov's systolic inequality bounds the length of the shortest non-contractible loop on a Riemannian manifold in terms of the volume of the manifold. Gromov's systolic inequality was proved in 1983; it can be viewed as a generalisation, albeit non-optimal, of Loewner's torus inequality and Pu's inequality for the real projective plane. where Cn is a universal constant only depending on the dimension of M.

Attributes	Values
rdf:type	yago:Abstraction100002137 yago:Attribute100024264 yago:Difference104748836 yago:Inequality104752221 yago:Quality104723816 yago:WikicatGeometricInequalities
rdfs:label	Gromov's systolic inequality for essential manifolds (en) Систолическое неравенство (ru)
rdfs:comment	In the mathematical field of Riemannian geometry, M. Gromov's systolic inequality bounds the length of the shortest non-contractible loop on a Riemannian manifold in terms of the volume of the manifold. Gromov's systolic inequality was proved in 1983; it can be viewed as a generalisation, albeit non-optimal, of Loewner's torus inequality and Pu's inequality for the real projective plane. where Cn is a universal constant only depending on the dimension of M. (en) Систолическое неравенство — неравенство следующего вида где есть замкнутое -мерное риманово многообразие в определённом классе, — длина кратчайшей нестягиваемой замкнутой кривой на (так называемая систола ) и — его объём. Как определённый класс обычно берётся топологический тип многообразия, но иногда рассматриваются, например, класс римановых многообразий конформно эквивалентных данному. (ru)
dcterms:subject	Systolic geometry Geometric inequalities Riemannian geometry
Wikipage page ID	12066797 (xsd:integer)
Wikipage revision ID	844519437 (xsd:integer)
Link from a Wikipage to another Wikipage	Annals of Mathematics Pu's inequality Systolic geometry Mathematics Essential manifold Contractible space Geometric inequalities Commentarii Mathematici Helvetici Fundamental class Fundamental group Systoles of surfaces Loewner's torus inequality American Mathematical Society Lens space Riemannian geometry Riemannian manifold Herbert Federer Riemannian geometry Systolic geometry Coarea formula Eilenberg–MacLane space Homology (mathematics) Filling area conjecture Filling radius Gromov's inequality for complex projective space Grushko theorem Gromov's inequality (disambiguation) Real projective space Aspherical manifold Mikhail Gromov (mathematician) Isoperimetry
sameAs	Gromov's systolic inequality for essential manifolds Gromov's systolic inequality for essential manifolds Gromov's systolic inequality for essential manifolds Gromov's systolic inequality for essential manifolds Gromov's systolic inequality for essential manifolds
dbp:wikiPageUsesTemplate	dbt:Citation dbt:Harvtxt dbt:Main dbt:Reflist dbt:Euclid dbt:Systolic_geometry_navbox
has abstract	In the mathematical field of Riemannian geometry, M. Gromov's systolic inequality bounds the length of the shortest non-contractible loop on a Riemannian manifold in terms of the volume of the manifold. Gromov's systolic inequality was proved in 1983; it can be viewed as a generalisation, albeit non-optimal, of Loewner's torus inequality and Pu's inequality for the real projective plane. Technically, let M be an essential Riemannian manifold of dimension n; denote by sysπ1(M) the homotopy 1-systole of M, that is, the least length of a non-contractible loop on M. Then Gromov's inequality takes the form where Cn is a universal constant only depending on the dimension of M. (en) Систолическое неравенство — неравенство следующего вида где есть замкнутое -мерное риманово многообразие в определённом классе, — длина кратчайшей нестягиваемой замкнутой кривой на (так называемая систола ) и — его объём. Как определённый класс обычно берётся топологический тип многообразия, но иногда рассматриваются, например, класс римановых многообразий конформно эквивалентных данному. Для многих топологических типов многообразий, например для произведения сферы и окружности систолическое неравенство не выполняется — существуют римановы метрики на с произвольно малым объёмом и произвольно длинной систолой. (ru)
prov:wasDerivedFrom	wikipedia-en:Gromov's_systolic_inequality_for_essential_manifolds?oldid=844519437&ns=0
page length (characters) of wiki page	5089 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Gromov's_systolic_inequality_for_essential_manifolds
is Link from a Wikipage to another Wikipage of	List of differential geometry topics List of inequalities Pu's inequality Essential manifold Loewner's torus inequality Systolic freedom Gromov's inequality Introduction to systolic geometry Larry Guth Systolic geometry Filling radius Gromov's inequality for complex projective space Mikhael Gromov (mathematician)
is known for of	Mikhael Gromov (mathematician)
is known for of	Mikhael Gromov (mathematician)
is foaf:primaryTopic of	wikipedia-en:Gromov's_systolic_inequality_for_essential_manifolds

Faceted Search & Find service v1.17_git139 as of Feb 29 2024

Alternative Linked Data Documents: ODE Content Formats:

RDF

ODATA

Microdata

About

OpenLink Virtuoso version 08.03.3330 as of Mar 19 2024, on Linux (x86_64-generic-linux-glibc212), Single-Server Edition (61 GB total memory, 49 GB memory in use)
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2024 OpenLink Software