Transverse equivalence of complete conformal foliations
A foliation \((M,F)\) is said to be conformal if it admits a transversal conformal structure. Any conformal foliation \((M,F)\) of codimension \(q > 2 \) either is Riemannian or has an attractor. The author first shows that if \( N \) is an arbitrary simply connected manifold, any countable subgroup of the group of diffeomorphisms of the manifold \(N\) is realized as the global holonomy group of some foliation covered by a fibration. Then she solves the classification problem for complete non-Riemannian conformal foliations of codimension \(q > 2\) with respect to transverse equivalence. As a consequence, she shows that the global holonomy group defined up to conjugation in the group \(\mathrm{Conf} (\mathbb S ^{q})\) is a complete invariant of the class of transversally equivalent non-Riemannian conformal foliations of codimension greater than 2. Several interesting examples are also presented.
non-Riemannian conformal foliation of codimension \(q>2\)
scientific article; zbMATH DE number 6497507