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

Chen, Qinbo; Damjanović, Danijela

doi:10.1090/tran/8896

Rigidity properties for some isometric extensions of partially hyperbolic actions on the torus
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by Qinbo Chen and Danijela Damjanović;

Trans. Amer. Math. Soc. 376 (2023), 4043-4083

DOI: https://doi.org/10.1090/tran/8896

Published electronically: March 21, 2023

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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 Kolmogorov-Arnold-Moser iterative scheme.

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