Title: Partially hyperbolic diffeomorphisms with one-dimensional neutral center on 3-manifolds,
Abstract: We prove that for any partially hyperbolic diffeomorphism with one
dimensional neutral center on a 3-manifold, the center stable and center
unstable foliations are complete; moreover, each leaf of center stable and
center unstable foliations is a cylinder, a M$\ddot{o}$bius band or a plane.
Further properties of the Bonatti-Parwani-Potrie type of partially hyperbolic
diffeomorphisms are studied. Such examples are obtained by composing the time
$m$-map (for $m>0$ large) of a non-transitive Anosov flow $\phi_t$ on an
orientable 3-manifold with Dehn twists along some transverse tori, and the
examples are partially hyperbolic with one-dimensional neutral center. We prove
that the center foliation gives a topologically Anosov flow which is
topologically equivalent to $\phi_t$. We also prove that for the precise
example constructed by Bonatti-Parwani-Potrie, the center stable and center
unstable foliations are robustly complete.