학술논문
Core reduction for singular Riemannian foliations in positive curvature
Document Type
Working Paper
Author
Source
Ann. Global Anal. Geom. 62 (2022) 617-634
Subject
Language
Abstract
We show that for a smooth manifold equipped with a singular Riemannian foliation, if the foliated metric has positive sectional curvature, and there exists a pre-section, that is a proper submanifold retaining all the transverse geometric information of the foliation, then the leaf space has boundary. In particular, we see that polar foliations of positively curved manifolds have leaf spaces with nonempty boundary.
Comment: 12 pages
Comment: 12 pages