Smooth Models for Certain Fibered Partially Hyperbolic Systems

Abstract

We prove that under restrictions on the fiber, any fibered partially hyperbolic system over a nilmanifold is leaf conjugate to a smooth model that is isometric on the fibers and descends to a hyperbolic nilmanifold automorphism on the base. One ingredient is a result of independent interest generalizing a result of Hiraide: an Anosov homeomorphism of a nilmanifold is topologically conjugate to a hyperbolic nilmanifold automorphism.

References in corpus (2)

• Pointwise partial hyperbolicity in 3-dimensional nilmanifolds
• The Gromoll filtration, KO-characteristic classes and metrics of positive scalar curvature