Non-negatively Curved Manifolds with Maximal Symmetry Rank in Low Dimensions

Abstract

We classify closed, simply-connected non-negatively curved 5-manifolds admitting an (almost) effective, isometric $T^3$ or $T^2$ action. As a direct consequence, we show that for any manifold, of dimensions up to and including 9 under the same hypotheses, the maximal symmetry rank is equal to $[2n/3]$ and the free rank is less than or equal to one half that value.

This paper has been revised and split into two papers. The first one ("Low-dimensional manifolds with non-negative curvature and maximal symmetry rank", Proc. A.M.S. 139 (2011), no. 7, 2559--2564) treats maximal symmetry rank. The second one (arXiv:1111.3183v1 [math.DG]) treats almost maximal sym. rank in dimension 5 and fixes an omission in the withdrawn submission (arXiv:0906.3870v1 [math.DG])

References in corpus (1)

• Finite extinction time for the solutions to the Ricci flow on certain three-manifolds

Cited by in corpus (1)

• Nonnegatively curved fixed point homogeneous 5-manifolds