We show that if a connected closed orientable manifold $M$ admits a codimension one locally free smooth action $\phi$ of a connected nilpotent Lie group such that any orbit of $\phi$ is non-compact, then $M$ is homeomorphic to a nilmanifold. And as an example of such an action, we study also a homogeneous action.
"On closed manifolds which admit codimension one locally free actions of nilpotent Lie groups." Hokkaido Math. J. 39 (1) 57 - 66, February 2010. https://doi.org/10.14492/hokmj/1274275019