Structure theory and convergence in Riemannian geometry

Jeff Cheeger

doi:10.1007/s00032-010-0117-4

Structure theory and convergence in Riemannian geometry

Jeff Cheeger

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We sketch a sequence of developments in riemannian geometry which have taken place over roughly the last 50 years. These concern structure theories for manifolds satisfying bounds on sectional or Ricci curvature, and related theories of geometric convergence. As an illustration, we describe some applications to the study of Einstein metrics in dimension 4.

Original language	English (US)
Pages (from-to)	221-264
Number of pages	44
Journal	Milan Journal of Mathematics
Volume	78
Issue number	1
DOIs	https://doi.org/10.1007/s00032-010-0117-4
State	Published - 2010

Keywords

Collapsing
Convergence
Einstein metric
Ricci curvature
Riemannian geometry
Rigidity
Sectional curvature

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1007/s00032-010-0117-4

Cite this

@article{f6a941a7d7044b33aff1947a32cc1fe3,

title = "Structure theory and convergence in Riemannian geometry",

abstract = "We sketch a sequence of developments in riemannian geometry which have taken place over roughly the last 50 years. These concern structure theories for manifolds satisfying bounds on sectional or Ricci curvature, and related theories of geometric convergence. As an illustration, we describe some applications to the study of Einstein metrics in dimension 4.",

keywords = "Collapsing, Convergence, Einstein metric, Ricci curvature, Riemannian geometry, Rigidity, Sectional curvature",

author = "Jeff Cheeger",

year = "2010",

doi = "10.1007/s00032-010-0117-4",

language = "English (US)",

volume = "78",

pages = "221--264",

journal = "Milan Journal of Mathematics",

issn = "1424-9286",

publisher = "Birkhauser Verlag Basel",

number = "1",

}

TY - JOUR

T1 - Structure theory and convergence in Riemannian geometry

AU - Cheeger, Jeff

PY - 2010

Y1 - 2010

N2 - We sketch a sequence of developments in riemannian geometry which have taken place over roughly the last 50 years. These concern structure theories for manifolds satisfying bounds on sectional or Ricci curvature, and related theories of geometric convergence. As an illustration, we describe some applications to the study of Einstein metrics in dimension 4.

AB - We sketch a sequence of developments in riemannian geometry which have taken place over roughly the last 50 years. These concern structure theories for manifolds satisfying bounds on sectional or Ricci curvature, and related theories of geometric convergence. As an illustration, we describe some applications to the study of Einstein metrics in dimension 4.

KW - Collapsing

KW - Convergence

KW - Einstein metric

KW - Ricci curvature

KW - Riemannian geometry

KW - Rigidity

KW - Sectional curvature

UR - http://www.scopus.com/inward/record.url?scp=77955335509&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77955335509&partnerID=8YFLogxK

U2 - 10.1007/s00032-010-0117-4

DO - 10.1007/s00032-010-0117-4

M3 - Article

AN - SCOPUS:77955335509

SN - 1424-9286

VL - 78

SP - 221

EP - 264

JO - Milan Journal of Mathematics

JF - Milan Journal of Mathematics

IS - 1

ER -

Structure theory and convergence in Riemannian geometry

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this