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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-Garcia
  • Martin Kerin
Article

Abstract

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.

Keywords

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

Mathematics Subject Classification (2000)

53C20 

Notes

Acknowledgments

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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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Mathematisches InstitutMünsterGermany

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