### Projectively Anosov flows with differentiable (un)stable foliations

We consider projectively Anosov flows with differentiable stable and unstable foliations. We characterize the flows on ${T}^{2}$ which can be extended on a neighbourhood of ${T}^{2}$ into a projectively Anosov flow so that ${T}^{2}$ is a compact leaf of the stable foliation. Furthermore, to realize this extension on an arbitrary closed 3-manifold, the topology of this manifold plays an essential role. Thus, we give the classification of projectively Anosov flows on ${T}^{3}$. In this case, the only flows on ${T}^{2}$ which extend to ${T}^{3}$...