Lefschetz pencil structures for 2-calibrated manifolds
A \(2\)-calibrated manifold is a smooth manifold \(M\) of dimension \(2n+1\) carrying a codimension \(1\) distribution \(D\) and a closed \(2\)-form \(\omega\) nondegenerate on \(D\). The authors generalize the notion of Lefschetz pencil structures on contact manifolds by \textit{F. Presas} [Asian J. Math. 6, No. 2, 277--302 (2002; Zbl 1101.53055)] to the notion on \(2\)-calibrated manifolds. They show that any closed \(2\)-calibrated manifold has a Lefschetz pencil structure and apply the result to taut foliations of \(3\)-dimensional manifolds.
scientific article; zbMATH DE number 2094049