Infinitesimally rigid Lie foliations with dense leaves

2024/03/26 by Stephane Geudens, Florian Zeiser, Geudens, Stephane +1
Mathematics · #53C12 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2403.17666

Abstract

We call a foliation F on a compact manifold infinitesimally rigid if its deformation cohomology H¹(F,NF) vanishes. This paper studies infinitesimal rigidity for a distinguished class of Riemannian foliations, namely Lie foliations with dense leaves. We construct infinitesimally rigid Lie foliations with dense leaves, modeled on any compact semisimple Lie algebra with simple ideals different from \mathfrakso(3). To our knowledge, these are the first examples of infinitesimally rigid Riemannian foliations that are not Hausdorff.

Citations

• Arithmetic Subgroups of Algebraic Groups

Related

• Rigidity of Lie affine foliations
• Rigidity of Lie foliations with locally symmetric leaves
• The diffeomorphism group of a Lie foliation
• Topological description of Riemannian foliations with dense leaves
• Singular Riemannian Foliations and the prescribing scalar curvature problem