Regular proiectively Anosov flows on the Seifert fibered 3-manifolds

Dedicated to Professor Yukio Matsumoto on his sixtieth birthday

Abstract

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