Energy and Riemannian Flows

We define and compute the energy of 1-foliations on riemannian manifolds. We then derive the Euler-Lagrange equations associated with the energy. We also prove that Riemannian flows on manifolds of constant curvature are ritical if and only if they are isometric. Finally we prove that isometric flows on 3-manifolds are critical if and only if either they are transverse to 2-dimensional foliations or they provide K-contact structures.