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

Fernando Galaz-Garcia; Catherine Searle

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arXiv · 0906.3870

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

Fernando Galaz-Garcia·Catherine Searle

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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.

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Fernando Galaz-Garcia, Catherine Searle. 2009-06-21. Non-negatively Curved Manifolds with Maximal Symmetry Rank in Low Dimensions. https://arxiv.org/abs/0906.3870

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