Positively curved manifolds with almost maximal symmetry rank

Xiaochun Rong

doi:10.1023/A:1021242512463

Positively curved manifolds with almost maximal symmetry rank

Xiaochun Rong

School of Arts and Sciences, Mathematics

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

37 Scopus citations

Abstract

The symmetry rank of a Riemannian manifold is the rank of the isometry group. We determine precisely which closed simply connected 5-manifolds admit positively curved metrics with (almost maximal) symmetry rank two. We also determine the precise Euler characteristic and the fundamental groups of all closed positively curved n-manifolds with almost maximal symmetry rank [(n - 1)/2] (n ≠ 6, 7).

Original language	English (US)
Pages (from-to)	157-182
Number of pages	26
Journal	Geometriae Dedicata
Volume	95
Issue number	1
DOIs	https://doi.org/10.1023/A:1021242512463
State	Published - 2002

All Science Journal Classification (ASJC) codes

Geometry and Topology

Keywords

Positive curvature
Singular set
Torus action

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title = "Positively curved manifolds with almost maximal symmetry rank",

abstract = "The symmetry rank of a Riemannian manifold is the rank of the isometry group. We determine precisely which closed simply connected 5-manifolds admit positively curved metrics with (almost maximal) symmetry rank two. We also determine the precise Euler characteristic and the fundamental groups of all closed positively curved n-manifolds with almost maximal symmetry rank [(n - 1)/2] (n ≠ 6, 7).",

keywords = "Positive curvature, Singular set, Torus action",

author = "Xiaochun Rong",

note = "Funding Information: $Supported partially by NSF Grant DMS 9971360 and Alfred P. Sloan Research Fellowship.",

year = "2002",

doi = "10.1023/A:1021242512463",

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T1 - Positively curved manifolds with almost maximal symmetry rank

AU - Rong, Xiaochun

N1 - Funding Information: $Supported partially by NSF Grant DMS 9971360 and Alfred P. Sloan Research Fellowship.

PY - 2002

Y1 - 2002

N2 - The symmetry rank of a Riemannian manifold is the rank of the isometry group. We determine precisely which closed simply connected 5-manifolds admit positively curved metrics with (almost maximal) symmetry rank two. We also determine the precise Euler characteristic and the fundamental groups of all closed positively curved n-manifolds with almost maximal symmetry rank [(n - 1)/2] (n ≠ 6, 7).

AB - The symmetry rank of a Riemannian manifold is the rank of the isometry group. We determine precisely which closed simply connected 5-manifolds admit positively curved metrics with (almost maximal) symmetry rank two. We also determine the precise Euler characteristic and the fundamental groups of all closed positively curved n-manifolds with almost maximal symmetry rank [(n - 1)/2] (n ≠ 6, 7).

KW - Positive curvature

KW - Singular set

KW - Torus action

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DO - 10.1023/A:1021242512463

M3 - Article

AN - SCOPUS:0036441792

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JO - Geometriae Dedicata

JF - Geometriae Dedicata

IS - 1

ER -

Positively curved manifolds with almost maximal symmetry rank

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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