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.