On conservative partially hyperbolic abelian actions with compact center foliation

Danijela Damjanovic; Disheng Xu

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arXiv · 1706.03626

On conservative partially hyperbolic abelian actions with compact center foliation

Danijela Damjanovic·Disheng Xu

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Abstract

We consider smooth partially hyperbolic volume preserving Z^k actions on smooth manifolds, with uniformly compact center foliation. We show that under certain irreducibility condition on the action, bunching and uniform quasiconformality conditions, the action is a smooth fiber bundle extension of an Anosov action, or the center foliation is pathological. We obtain several corollaries of this result. For example, we prove a global dichotomy result that any smooth conservative circle extension over a maximal Cartan action is either essentially a product of an action by rotations and a linear Anosov action on the torus, or has a pathological center foliation.

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Danijela Damjanovic, Disheng Xu. 2017-06-12. On conservative partially hyperbolic abelian actions with compact center foliation. https://arxiv.org/abs/1706.03626

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