On the completeness of dual foliations on nonnegatively curved symmetric spaces

TL;DR

This paper proves Wilking's Conjecture regarding the completeness of dual leaves in Riemannian foliations on nonnegatively curved symmetric spaces, showing they split into trivial and single-leaf foliations.

Contribution

It establishes the completeness of dual leaves in this setting and describes the foliation structure as a product of trivial and single-leaf components.

Findings

Proof of Wilking's Conjecture for nonnegatively curved symmetric spaces

Dual foliations split as a product of trivial and single-leaf foliations

Enhanced understanding of foliation structure in symmetric spaces

Abstract

We prove Wilking's Conjecture about the completeness of dual leaves for the case of Riemannian foliations on nonnegatively curved symmetric spaces. Moreover, we conclude that such foliations split as a product of trivial foliations and a foliation with a single dual leaf.