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

Galaz-Garcia, Fernando; Searle, Catherine

doi:10.1090/S0002-9939-2010-10655-X

Low-dimensional manifolds with non-negative curvature and maximal symmetry rank
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by Fernando Galaz-Garcia and Catherine Searle PDF

Proc. Amer. Math. Soc. 139 (2011), 2559-2564 Request permission

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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