# Hokkaido Mathematical Journal

## Hokkaido Mathematical Journal, 39 (2010) pp.57-66

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### Abstract

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.

MSC(Primary) 37C85(MSC2000), 57R30(MSC2000), 57S20(MSC2000) locally free action; foliation; nilpotent Lie group;