Veronese webs and transversally Veronese foliations (Q2782011)

A web on a surface \(S\) consists of three codimension-one foliations, which are transversal to each other everywhere on \(S\). A foliated web on a 3-manifold \(M\) is a flow consisting of the intersection of three codimension-one foliations, which are transversal to each other everywhere on \(M\). Now, a conformally parallelizable (CP) structure on an \(n\)-dimensional manifold \(M\) corresponds to \(n+1\) foliations of dimension 1, whose associated directions are mutually transversal, and span the entire tangent space \(T_XM\) at every point \(X\in M\). In this paper some elementary facts concerning these structures and their rigidity are studied and the foliations possessing a transversally CP structure are considered. Finally classifications of the transversally CP flows and applications to bi-Hamiltonian systems in odd dimension are given.NEWLINENEWLINEFor the entire collection see [Zbl 0983.00024].