Tohoku Mathematical Journal

Codimension one locally free actions of solvable Lie groups

Aiko Yamakawa and Nobuo Tsuchiya

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Let $G$ be a non-unimodular solvable Lie group which is a semidirect product of $R^m$ and $R^n$. We consider a codimension one locally free volume preserving action of $G$ on a closed manifold. It is shown that, under some conditions on the group $G$, such an action is homogeneous. It is also shown that such a group $G$ has a homogeneous action if and only if the structure constants of $G$ satisfy certain algebraic conditions.

Article information

Tohoku Math. J. (2), Volume 53, Number 2 (2001), 241-263.

First available in Project Euclid: 3 May 2007

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Zentralblatt MATH identifier

Primary: 37C85: Dynamics of group actions other than Z and R, and foliations [See mainly 22Fxx, and also 57R30, 57Sxx]
Secondary: 22F30: Homogeneous spaces {For general actions on manifolds or preserving geometrical structures, see 57M60, 57Sxx; for discrete subgroups of Lie groups, see especially 22E40}


Yamakawa, Aiko; Tsuchiya, Nobuo. Codimension one locally free actions of solvable Lie groups. Tohoku Math. J. (2) 53 (2001), no. 2, 241--263. doi:10.2748/tmj/1178207480.

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