On Riemannian Foliations over Positively Curved Manifolds

TL;DR

This paper proves that certain types of Riemannian foliations are impossible in positively curved manifolds, advancing understanding of geometric structures in such spaces.

Contribution

It establishes a non-existence result for odd co-dimension Riemannian foliations in positively curved manifolds under specific conditions.

Findings

Odd co-dimension Riemannian foliations cannot occur in positively curved manifolds

Provides conditions under which such foliations are impossible

Enhances understanding of geometric constraints in positively curved spaces

Abstract

We prove that, under reasonable conditions, odd co-dimension Riemannian foliations cannot occur in positively curved manifolds.