A curvature approach to fatness

TL;DR

This paper investigates the geometric properties of fat Riemannian submersions, classifying fibers, establishing isometric correspondences, and demonstrating rigidity, thereby advancing understanding of curvature and foliation structures in differential geometry.

Contribution

It introduces a curvature-based approach to classify and analyze fat Riemannian submersions, revealing their fiber structures and rigidity properties.

Findings

Fibers are symmetric spaces.

Fat foliations correspond to coset foliations on Lie groups.

Dual foliations exhibit rigidity.

Abstract

This paper delves into the concept of ``fat bundles'' within Riemannian submersions. One explores the structural implications of fat Riemannian submersions, particularly focusing on those with non-negative sectional curvature. The main results include the classification of fibers as symmetric spaces, the isometric correspondence of fat foliations with coset foliations on Lie groups, and the rigidity of dual foliations associated with fat Riemannian submersions.