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

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

2009-06-21

arxiv.org/abs/0906.3870v3

Mathematics

Differential Geometry

This paper has been revised and split into two papers. The first one ("Low-dimensional manifolds with non-negative curvature a

Scientific paper

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.

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