Singular Riemannian flows and characteristic numbers (Q670322)

This work is concerned with singular Riemannian foliations generated by a single vector field, on an even dimensional, closed and oriented manifold $M$. In other words, the maximal dimension of each leaf is one. The authors first describe the foliation around a singular stratum: It always comes from the action of an orthogonal group. Using this, they generalise the formula given by \textit{P. F. Baum} and \textit{J. Cheeger} [Topology 8, 173--193 (1969; Zbl 0179.28802)] for the characteristic numbers of the manifold $M$.