Positively curved manifolds with almost maximal symmetry rank

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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
Issue number1
StatePublished - 2002

All Science Journal Classification (ASJC) codes

  • Geometry and Topology


  • Positive curvature
  • Singular set
  • Torus action


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