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).
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Rong, X. Positively Curved Manifolds with Almost Maximal Symmetry Rank. Geometriae Dedicata 95, 157–182 (2002). https://doi.org/10.1023/A:1021242512463
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DOI: https://doi.org/10.1023/A:1021242512463