2025/05/23 by Meigniez, Gael, Nozawa, Hiraku
#37C85 #53C12 #53C24 #57R30 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.2505.17633
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.