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).
All Science Journal Classification (ASJC) codes
- Geometry and Topology
- Positive curvature
- Singular set
- Torus action