Incompressible surfaces and pseudo-Anosov flows

As the main result of this paper, we show that any closed surface immersed transverse to a suitable pseudo-Anosov flow on a closed, hyperbolic three-manifold is geometrically infinite if and only if the surface lifts to be an embedded fiber in a finite cover in which the flow lifts to be the suspension flow. This is an extension of results known for surfaces immersed in bundles (Cooper et al., 1994).