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arXiv · 2505.17633

Rigidity of Lie foliations with locally symmetric leaves

Gael Meigniez·Hiraku Nozawa
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Abstract

We prove that if the leaves of a minimal Lie foliation are locally isometric to a symmetric space of non-compact type without a Poincare disk factor, then the foliation is smoothly conjugate to a homogeneous Lie foliation up to finite covering. This result generalizes and strengthens Zimmer's theorem, which characterizes minimal Lie foliations with leaves isometric to a symmetric space of non-compact type without real rank one factors as pullbacks of homogeneous foliations. As applications, we extend Zimmer's arithmeticity theorem for holonomy groups and establish a rigidity theorem for Riemannian foliations with locally symmetric leaves.

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Gael Meigniez, Hiraku Nozawa. 2025-05-23. Rigidity of Lie foliations with locally symmetric leaves. https://arxiv.org/abs/2505.17633

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