Rigidity properties for some isometric extensions of partially hyperbolic actions on the torus

Qinbo Chen; Danijela Damjanović

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arXiv · 2202.05091

Rigidity properties for some isometric extensions of partially hyperbolic actions on the torus

Qinbo Chen·Danijela Damjanović

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Abstract

This paper studies local rigidity for some isometric toral extensions of partially hyperbolic $\mathbb{Z}^k$ ($k\geqslant 2$) actions on the torus. We prove a $C^\infty$ local rigidity result for such actions, provided that the smooth perturbations of the actions satisfy the intersection property. We also give a local rigidity result within a class of volume preserving actions. Our method mainly uses a generalization of the KAM iterative scheme.

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BibTeX RIS

Qinbo Chen, Danijela Damjanović. 2022-02-10. Rigidity properties for some isometric extensions of partially hyperbolic actions on the torus. https://arxiv.org/abs/2202.05091

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