The automorphism groups of foliations with transverse linear connection (Q2440523)

The foliated bundle of transverse frames with the lifted foliation is applied for the construction of a special linear connection for an arbitrary smooth foliation \((M,F)\). The authors prove that the automorphism group \(\mathcal{D}(M,F)\) of a foliation \((M,F)\) with transverse linear connection is an infinite-dimensional Lie group modeled on LF-spaces. As pseudo-Riemannian foliations belong to the class of foliations with transverse linear connection, the above mentioned property concerning the automorphism group of a foliation is also valid for pseudo-Riemannian and Lorentzian foliations.