Singular Riemannian foliations and collapse

2025/03/30 by Corro, Diego
#22A22 #32G99 #53C12 #53C20 #53C21 #53C23 #57R30 #58H05 #58H15 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2503.23562

Abstract

In this survey we present classical results on methods to use group actions to collapse manifolds to the orbit spaces while keeping some control on the curvature, and recent extensions of these constructions to the setting of singular Riemannian foliations.

Related

• Singular Riemannian Foliations and the prescribing scalar curvature problem
• Collapsing regular Riemannian foliations with flat leaves
• Low dimensional Singular Riemannian Foliations in spheres
• Blown-up singular Riemannian foliations
• The dual foliation of some singular Riemannian foliations