Solvable Lie flows of codimension 3

Abstract

In Appendix E of Riemannian foliations [Progress in Mathematics 73, Birkhäuser, Boston (1988)], É Ghys proved that any Lie g-flow is homogeneous if g is a nilpotent Lie algebra. In the case where g is solvable, we expect any Lie g-flow to be homogeneous. In this paper, we study this problem in the case where g is a 3-dimensional solvable Lie algebra.