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

Smooth Models for Certain Fibered Partially Hyperbolic Systems