Conformal subfoliations of prescribed geodesic curvature

Abstract

Given a $2$-dimensional conformal foliation $\mathcal F$ of a Riemannian manifold $M$, the problem of finding a $1$-dimensional subfoliation $\mathcal G$, conformal in $M$, whose leaves have prescribed geodesic curvature in the leaves of $\mathcal F$ is equivalent to a Pfaff differential system on a circle bundle over $M$. We study such pairs of foliations on a $3$- and $4$-manifold.