This paper concerns projectively Anosov flows with smooth stable and unstable foliations and on a Seifert fibered 3-manifold over a hyperbolic orbifold. We show that if the foliations and do not have compact leaves, then after changing the parameter, is differentiably isotopic to a quasi-Fuchsian flow lifted to a finite cover.
Takashi TSUBOI. "Regular projectively Anosov flows on the Seifert fibered 3-manifolds." J. Math. Soc. Japan 56 (4) 1233 - 1253, October, 2004. https://doi.org/10.2969/jmsj/1190905458