Hokkaido Mathematical Journal

On closed manifolds which admit codimension one locally free actions of nilpotent Lie groups

Yo-ichi MORIYAMA

Full-text: Open access

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.

Article information

Source
Hokkaido Math. J., Volume 39, Number 1 (2010), 57-66.

Dates
First available in Project Euclid: 19 May 2010

Permanent link to this document
https://projecteuclid.org/euclid.hokmj/1274275019

Digital Object Identifier
doi:10.14492/hokmj/1274275019

Mathematical Reviews number (MathSciNet)
MR2649326

Zentralblatt MATH identifier
1202.37024

Subjects
Primary: 37C85: Dynamics of group actions other than Z and R, and foliations [See mainly 22Fxx, and also 57R30, 57Sxx]
Secondary: 57R30: Foliations; geometric theory 57S20: Noncompact Lie groups of transformations

Keywords
locally free action foliation nilpotent Lie group

Citation

MORIYAMA, Yo-ichi. On closed manifolds which admit codimension one locally free actions of nilpotent Lie groups. Hokkaido Math. J. 39 (2010), no. 1, 57--66. doi:10.14492/hokmj/1274275019. https://projecteuclid.org/euclid.hokmj/1274275019


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