In Appendix E of Riemannian foliations [Progress in Mathematics 73, Birkhäuser, Boston (1988)], É Ghys proved that any Lie –flow is homogeneous if is a nilpotent Lie algebra. In the case where is solvable, we expect any Lie –flow to be homogeneous. In this paper, we study this problem in the case where is a –dimensional solvable Lie algebra.
"Solvable Lie flows of codimension $3$." Algebr. Geom. Topol. 16 (5) 2751 - 2778, 2016. https://doi.org/10.2140/agt.2016.16.2751