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

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.