Lie flows of codimension 3

Abstract

We study the following realization problem: given a Lie algebra of dimension 3 3 and an integer q , 0 ≤ q ≤ 3 q,0 \leq q \leq 3 , is there a compact manifold endowed with a Lie flow transversely modeled on G \mathcal {G} and with structural Lie algebra of dimension q q ? We give here a quite complete answer to this problem but some questions remain still open ( cf. § 2 ({\text {cf.}}\;\S 2 .