The dual foliation of some singular Riemannian foliations

TL;DR

This paper applies subriemannian geometry techniques to analyze the dual foliation of singular Riemannian foliations generated by Lie group actions, demonstrating conditions under which the dual foliation consists of a single leaf.

Contribution

It introduces a novel approach using subriemannian geometry to study dual foliations in the context of singular Riemannian foliations induced by Lie group actions.

Findings

Dual foliation has only one leaf under certain conditions.

Uses subriemannian geometry methods in foliation analysis.

Provides new insights into the structure of singular Riemannian foliations.

Abstract

In this paper, we use the methods of subriemannian geometry to study the dual foliation of the singular Riemannian foliation induced by isometric Lie group actions on a complete Riemannian manifold M. We show that under some conditions, the dual foliation has only one leaf.