On a classification of fat bundles over compact homogeneous spaces

TL;DR

This paper investigates the classification of fat bundles over compact homogeneous spaces, extending Berard-Bergery's work, and provides necessary conditions for their existence in the context of G-structures with canonical connections.

Contribution

It generalizes the classification of fat bundles to arbitrary G-structures over homogeneous spaces, offering necessary conditions for their existence.

Findings

Derived necessary conditions for fat bundle existence

Extended classification framework for G-structures

Connected results to Berard-Bergery's classification

Abstract

This article deals with fat bundles. Berard-Bergery classified all homogeneous bundles of that type. We ask a question of a possibility to generalize his description in the case of arbitrary G-structures over homogeneous spaces. We obtain necessary conditions for the existence of such bundles. These conditions yield a kind of classification of fat bundles associated with G-structures over compact homogeneous spaces provided that the connection in a G-structure is canonical.