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

2009/06/21 by Fernando Galaz‐García, Fernando Galaz-Garcia, Galaz-Garcia, Fernando +2 · 1 citation
Mathematics · #51M25 (Secondary) #53C20 (Primary) #57S25 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations #math.DG #msc:51M25 #msc:53C20 #msc:57S25

paper · pdf · doi:10.48550/arxiv.0906.3870

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 rank in dimension 5 and fixes an omission in the withdrawn submission (arXiv:0906.3870v1 [math.DG])

openalex publication_date 2009/06/21 · arxiv created 2011/11/17 · arxiv updated 2011/11/18 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We classify closed, simply-connected non-negatively curved 5-manifolds admitting an (almost) effective, isometric T³ or T² 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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• Non-negatively curved 5-manifolds with almost maximal symmetry rank

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