About: Soul theorem

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In mathematics, the soul theorem is a theorem of Riemannian geometry that largely reduces the study of complete manifolds of non-negative sectional curvature to that of the compact case. Jeff Cheeger and Detlef Gromoll proved the theorem in 1972 by generalizing a 1969 result of Gromoll and Wolfgang Meyer. The related soul conjecture, formulated by Cheeger and Gromoll at that time, was proved twenty years later by Grigori Perelman.

Attributes	Values
rdf:type	yago:WikicatTheoremsInRiemannianGeometry yago:Abstraction100002137 yago:Communication100033020 yago:Message106598915 yago:Proposition106750804 yago:Statement106722453 yago:Theorem106752293
rdfs:label	Seelensatz (de) Théorème de l'âme (fr) Teorema di Cheeger-Gromoll (it) 영혼 (기하학) (ko) Soul theorem (en) Душа (дифференциальная геометрия) (ru)
rdfs:comment	Der Seelensatz ist ein mathematischer Lehrsatz aus dem Gebiet der Differentialgeometrie, der es ermöglicht, die Untersuchung von (nicht-kompakten) Mannigfaltigkeiten nichtnegativer Krümmung auf die Untersuchung von Vektorbündeln über kompakten Mannigfaltigkeiten nichtnegativerKrümmung zurückzuführen. Er wurde von Jeff Cheeger und Detlef Gromoll sowiein seiner verschärften Form (für in mindestens einem Punkt positive Krümmung) von Grigori Perelman bewiesen. (de) In mathematics, the soul theorem is a theorem of Riemannian geometry that largely reduces the study of complete manifolds of non-negative sectional curvature to that of the compact case. Jeff Cheeger and Detlef Gromoll proved the theorem in 1972 by generalizing a 1969 result of Gromoll and Wolfgang Meyer. The related soul conjecture, formulated by Cheeger and Gromoll at that time, was proved twenty years later by Grigori Perelman. (en) En géométrie riemannienne, le théorème de l'âme concerne la structure des espaces à courbure positive, la réduisant dans une large mesure à l'étude du cas compact. Le terme d'âme est une allusion à l', donnant l'image d'une structure « recourbée sur elle-même » se prolongeant dans une certaine direction « à la manière d'un cylindre ». Le théorème a été prouvé par Cheeger et Gromoll en 1972, généralisant un premier résultat de Gromoll et (de) de 1969. Un cas limite a été proposé sous forme de conjecture par Gromoll et Meyer en 1972, cette conjecture de l'âme a été prouvée par Grigori Perelman en 1994. (fr) 리만 기하학에서 영혼(靈魂, 영어: soul 솔[*])은 음이 아닌 단면 곡률을 갖는 리만 다양체에 대하여 존재하는 특별한 콤팩트 부분 다양체이다. 이를 통해, 음이 아닌 단면 곡률을 갖는 다양체의 연구는 콤팩트한 경우로 귀결된다. (ko) Душа риманова многообразия — компактное подмногообразие, являющееся его деформационным ретрактом. Обычно предполагается, что — полное связное риманово многообразие с секционной кривизной K ≥ 0. (ru) Il teorema di Cheeger-Gromoll, o Soul Theorem (in italiano Teorema dell'anima), è un teorema di Geometria riemanniana che in larga misura riconduce lo studio delle varietà geometriche complete di curvatura sezionale non negative al caso delle varietà compatte (chiuse e finite). Jeff Cheeger e Detlef Gromoll dimostrarono il teorema nel 1972 generalizzando un risultato ottenuto nel 1969 dallo stesso Gromoll e da Wolfgang Meyer. La correlata congettura dell'anima (Soul conjecture) fu formulata da Gromoll e Cheeger nel 1972, e dimostrata da Grigorij Jakovlevič Perel'man nel 1994 in un modo sorprendente e conciso. (it)
dcterms:subject	Theorems in Riemannian geometry
Wikipage page ID	936932 (xsd:integer)
Wikipage revision ID	1087038195 (xsd:integer)
Link from a Wikipage to another Wikipage	Theorems in Riemannian geometry Princeton University Press Detlef Gromoll Annals of Mathematics Compact space Complete space Mathematics Chelsea Publishing Company Connected space Lipschitz map Closed manifold Gauss-Codazzi equations Springer Publishing Mathematical Surveys and Monographs American Mathematical Society Cylinder (geometry) Euclidean space Paraboloid Diffeomorphism Glossary of Riemannian and metric geometry Graduate Texts in Mathematics Journal of Differential Geometry Retraction (topology) Riemannian geometry Riemannian manifold Riemannian submersion Grigori Perelman Isometry Jeff Cheeger Manifold Vector bundle Sharafutdinov's retraction Sectional curvature Embedded submanifold Compact manifold Submetry
Link from a Wikipage to an external page	https://projecteuclid.org/download/pdf_1/euclid.jdg/1214455292 https://semanticscholar.org/paper/2906e408f5668b32182e60ab0c431483354b0ffa
sameAs	Soul theorem Soul theorem Soul theorem Soul theorem Soul theorem Soul theorem Soul theorem Soul theorem Soul theorem Soul theorem
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3loc	Theorem V.3.4 (en)
1a	Petersen (en) Sakai (en) Chow (en) Chu (en) Yau (en) Ebin (en) Cheeger (en) Guenther (en) Glickenstein (en)
1loc	Chapter 8 (en) Example 12.4.3 (en) Example 12.4.4 (en) Problem 6 (en) Theorem I.25 (en)
1p	217 (xsd:integer) 462 (xsd:integer) 469 (xsd:integer)
1y	1982 (xsd:integer)

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