Non-unimodular Lie foliations

Non-unimodular transversely homogeneous foliations

“…By applying the results of the first part of the paper to this new foliated structure, we are able to prove in all generality the characterization of unimodular foliations (Theorem 5.17) and Theorem 1.3 cited above. These results generalize analogous results for Lie foliations that we announced in [17].…”

“…This will allow us to prove the Theorem 1.3 that we stated in the Introduction, which is our main result in the second part of the paper, and that generalizes an analogous result that we proved for Lie foliations in [17].…”

“…El Kazimi Alaoui and Nicolau went further in the study of the unimodularity of Lie foliations and proved the following result. Finally, we have proved in [17] the following result, which is now a particular case of our Theorem 1.3, when restricted to Lie foliations. Theorem 6.19.…”

“…On the other hand, if det Ad Γ (γ) = −1 for some γ, we can consider, as we did in [17], the subgroup H 2 = {γ ∈ Γ : det Ad Γ (γ) > 0} and the manifold W 2 = H 2 \G . In this way, W 2 is compact and det Ad H2 (h) = 1 = det Ad G (h) for all h ∈ H 2 .…”

Non-unimodular transversely homogeneous foliations

“…By applying the results of the first part of the paper to this new foliated structure, we are able to prove in all generality the characterization of unimodular foliations (Theorem 5.17) and Theorem 1.3 cited above. These results generalize analogous results for Lie foliations that we announced in [18].…”