Collapsing regular Riemannian foliations with flat leaves

2024/03/18 by Corro, Diego
#53C12 #53C20 #53C23 #53C24 #57R30 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2403.11602

Abstract

We present how to collapse a manifold equipped with a closed flat regular Riemannian foliation with leaves of positive dimension on a compact manifold, while keeping the sectional curvature uniformly bounded from above and below. From this deformation, we show that a closed flat regular Riemannian foliation with leaves of positive dimension on a compact simply-connected manifold is given by torus actions. This gives a geometric characterization of aspherical regular Riemannian foliations given by torus actions.

Related

• Singular Riemannian foliations and collapse
• The closure of linear foliations
• Compact leaves in Reebless or taut foliations
• A-Foliations of codimension two on compact simply-connected manifolds
• Topological description of Riemannian foliations with dense leaves