Leaves of foliations with a transverse geometric structure of finite type (Q1824247)

A G-foliation \({\mathcal F}\) of a compact manifold M is of finite type when its prolongation \({\mathcal F}_ k\) to the total space \(B^{k-1}(M,G,{\mathcal F})\) of the prolongation of the foliated reduction B(M,G,\({\mathcal F})\) of the bundle L(M,\({\mathcal F})\) of transverse linear frames of \({\mathcal F}\) is transversely parallelizable. The main result says that if \({\mathcal F}\) is transversely complete and of finite type then its space of leaves is a Satake manifold iff all the leaves of \({\mathcal F}\) are compact.