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Low-dimensional manifolds with non-negative curvature and maximal symmetry rank

Authors: Fernando Galaz-Garcia and Catherine Searle
Journal: Proc. Amer. Math. Soc. 139 (2011), 2559-2564
MSC (2010): Primary 53C20; Secondary 57S25
Published electronically: December 3, 2010
MathSciNet review: 2784821
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Abstract: We classify closed, simply connected $ n$-manifolds of non-negative sectional curvature admitting an isometric torus action of maximal symmetry rank in dimensions $ 2\leq n\leq 6$. In dimensions $ 3k$, $ k=1,2$ there is only one such manifold and it is diffeomorphic to the product of $ k$ copies of the $ 3$-sphere.

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Fernando Galaz-Garcia
Affiliation: Mathematisches Institut, Westfälische Wilhelms-Universität Münster, 48149 Münster, Germany

Catherine Searle
Affiliation: Instituto de Matematicas, Unidad Cuernavaca, Universidad Autónoma de México, Cuernavaca, Morelos, Mexico

Received by editor(s): April 21, 2010
Received by editor(s) in revised form: June 7, 2010, and June 17, 2010
Published electronically: December 3, 2010
Additional Notes: The authors thank the American Institute of Mathematics (AIM) for its support during a workshop where the work on this paper was initiated.
The second author was supported in part by CONACYT Project #SEP-CO1-46274, CONACYT Project #SEP-82471 and UNAM DGAPA project IN-115408.
Communicated by: Jianguo Cao
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.