Mathematische Zeitschrift

, Volume 276, Issue 1–2, pp 133–152 | Cite as

Cohomogeneity-two torus actions on non-negatively curved manifolds of low dimension

  • Fernando Galaz-GarciaEmail author
  • Martin Kerin


Let \(\mathrm{M }^n,\, n \in \{4,5,6\}\), be a compact, simply connected \(n\)-manifold which admits some Riemannian metric with non-negative curvature and an isometry group of maximal possible rank. Then any smooth, effective action on \(\mathrm{M }^n\) by a torus \(\mathrm{T }^{n-2}\) is equivariantly diffeomorphic to an isometric action on a normal biquotient. Furthermore, it follows that any effective, isometric circle action on a compact, simply connected, non-negatively curved four-dimensional manifold is equivariantly diffeomorphic to an effective, isometric action on a normal biquotient.


Non-negative curvature Circle action Torus action 4-manifolds 5-manifolds Symmetry rank 

Mathematics Subject Classification (2000)




The first named author thanks B. Wilking and K. Grove for useful conversations. The second named author wishes to thank J. DeVito for several interesting and helpful discussions.


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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Mathematisches InstitutMünsterGermany

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