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:Inequality104752221, 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:Quality104723816 yago:WikicatGeometricInequalities yago:Abstraction100002137 yago:Attribute100024264 yago:Difference104748836 yago:Inequality104752221
rdfs:label	Gromov's systolic inequality for essential manifolds
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.
foaf:isPrimaryTopicOf	wikipedia-en:Gromov's_systolic_inequality_for_essential_manifolds
dct: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	Contractible space Real projective space Lens space Gromov's inequality Gromov's inequality for complex projective space Grushko theorem Homology (mathematics) Systolic geometry Riemannian geometry Filling area conjecture Filling radius Fundamental class Fundamental group Geometric inequalities Essential manifold Mikhael Gromov (mathematician) Loewner's torus inequality American Mathematical Society Riemannian manifold Herbert Federer Commentarii Mathematici Helvetici Riemannian geometry Aspherical space Systolic geometry Isoperimetric inequality Eilenberg–MacLane space Annals of Mathematics Mathematics Pu's inequality Coarea formula Systoles of surfaces
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
dbp:wikiPageUsesTemplate	dbt:Systolic_geometry_navbox dbt:Citation dbt:Harvtxt dbt:Main dbt:Reflist dbt:Euclid
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.
prov:wasDerivedFrom	wikipedia-en:Gromov's_systolic_inequality_for_essential_manifolds?oldid=844519437&ns=0
page length (characters) of wiki page	5089(xsd:integer)
is foaf:primaryTopic of	wikipedia-en:Gromov's_systolic_inequality_for_essential_manifolds
is Link from a Wikipage to another Wikipage of	Gromov's inequality Gromov's inequality for complex projective space Larry Guth Systolic freedom Filling radius Essential manifold Mikhael Gromov (mathematician) Loewner's torus inequality Introduction to systolic geometry Systolic geometry List of differential geometry topics List of inequalities Pu's inequality

Faceted Search & Find service v1.17_git51 as of Sep 16 2020

Alternative Linked Data Documents: PivotViewer | iSPARQL | ODE Content Formats:

RDF

ODATA

Microdata

About

OpenLink Virtuoso version 08.03.3319 as of Dec 29 2020, on Linux (x86_64-centos_6-linux-glibc2.12), Single-Server Edition (61 GB total memory)
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2021 OpenLink Software