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Conformal subfoliations of prescribed geodesic curvature

2003; Aarhus University Library; Volume: 93; Issue: 2 Linguagem: Inglês

10.7146/math.scand.a-14420

1903-1807

Paul Baird, Jean‐Marie Burel,

Mathematical Dynamics and Fractals

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.