Some curvature estimates for Riemannian manifolds equipped with foliations of rank 2

TL;DR

This paper derives curvature estimates for Riemannian manifolds with rank 2 foliations using geometric data related to quasi-conformality of certain vector fields, advancing understanding of curvature behavior in such structures.

Contribution

It introduces new curvature estimates based on quasi-conformality properties of commuting vector fields on compact Riemannian manifolds.

Findings

Derived curvature bounds from quasi-conformal vector fields.

Connected geometric properties to curvature estimates.

Enhanced understanding of curvature in rank 2 foliated manifolds.

Abstract

Some curvature estimates are derived from geometrical data concerning quasi-conformality properties of some commuting linearly independent vector fields on a compact Riemannian manifold.