Positively curved manifolds with almost maximal symmetry rank

Research output: Contribution to journalArticle

33 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)157-182
Number of pages26
JournalGeometriae Dedicata
Volume95
Issue number1
DOIs
StatePublished - Dec 1 2002

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Symmetry
Closed
Isometry Group
Euler Characteristic
Fundamental Group
Riemannian Manifold
Metric

All Science Journal Classification (ASJC) codes

  • Geometry and Topology

Keywords

  • Positive curvature
  • Singular set
  • Torus action

Cite this

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Positively curved manifolds with almost maximal symmetry rank. / Rong, Xiaochun.

In: Geometriae Dedicata, Vol. 95, No. 1, 01.12.2002, p. 157-182.

Research output: Contribution to journalArticle

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