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

Galaz-Garcia, Fernando; Kerin, Martin

Abstract

Let Mn, n ∈ {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 Mn by a torus Tn−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, nonnegatively curved four-dimensional manifold is equivariantly diffeomorphic to an effective, isometric action on a normal biquotient.

Citation

Galaz-Garcia, F., & Kerin, M. (2014). Cohomogeneity-two torus actions on non-negatively curved manifolds of low dimension. Mathematische Zeitschrift, 276(1-2), 133-152. https://doi.org/10.1007/s00209-013-1190-5

• Journal Article Type: Article
• Acceptance Date: May 12, 2013
• Online Publication Date: Jul 11, 2013
• Publication Date: 2014-02
• Deposit Date: Dec 12, 2019
• Publicly Available Date: Nov 15, 2022
• Journal: Mathematische Zeitschrift
• Print ISSN: 0025-5874
• Electronic ISSN: 1432-1823
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Volume: 276
• Issue: 1-2
• Pages: 133-152
• DOI: https://doi.org/10.1007/s00209-013-1190-5
• Related Public URLs: https://arxiv.org/abs/1111.1640