Regular projectively Anosov flows on the Seifert fibered 3-manifolds

Abstract

This paper concerns projectively Anosov flows ${\phi }_t$ with smooth stable and unstable foliations ${\mathcal{F}}^S$ and ${\mathcal{F}}^{\mathsf{U}}$ on a Seifert fibered 3-manifold $M$ over a hyperbolic orbifold. We show that if the foliations ${\mathcal{F}}^S$ and ${\mathcal{F}}^{\mathsf{U}}$ do not have compact leaves, then after changing the parameter, ${\phi }_t$ is differentiably isotopic to a quasi-Fuchsian flow lifted to a finite cover.