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

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

2011-11-07

arxiv.org/abs/1111.1640v1

Mathematics

Differential Geometry

Scientific paper

Let $M^n$, $n \in \{4,5,6\}$, 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 $M^n$ by a torus $T^{n-2}$ 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.

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