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

Fernando Galaz-Garcia; Catherine Searle

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

Differential Geometry 2012-07-27 v1

Authors: Fernando Galaz-Garcia , Catherine Searle

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.

Keywords

low-dimensional manifolds non-negative sectional curvature maximal symmetry rank isometric torus action classification simply connected 3-sphere

Cite

@article{arxiv.1207.6173,
  title  = {Low-dimensional manifolds with non-negative curvature and maximal symmetry rank},
  author = {Fernando Galaz-Garcia and Catherine Searle},
  journal= {arXiv preprint arXiv:1207.6173},
  year   = {2012}
}

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