Tohoku Mathematical Journal
2001
June
SECOND SERIES VOL. 53, NO. 2

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

Title CODIMENSION ONE LOCALLY FREE ACTIONS OF SOLVABLE LIE GROUPS

Author Aiko Yamakawa and Nobuo Tsuchiya

(Received July 19, 1999, revised September 6, 2000)
Abstract. Let $G$ be a non-unimodular solvable Lie group which is a semidirect product of $\boldsymbol{R}^m$ and $\boldsymbol{R}^n$. 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.

2000 Mathematics Subject Classification. Primary 37C85, Secondary 22F30.

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