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

Abstract

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.

References in corpus (1)

• Ricci flow with surgery on three-manifolds

Cited by in corpus (1)

• Simply connected Alexandrov 4-manifolds with positive or nonnegative curvature and torus actions