Projectively flat connections and flat connections on homogeneous spaces

TL;DR

This paper establishes a correspondence between G-invariant projectively flat connections on a homogeneous space and G~-invariant flat connections on a related space, via a central extension of the group G.

Contribution

It introduces a novel correspondence linking projectively flat and flat connections on homogeneous spaces through central extensions.

Findings

Established a bijective correspondence between the two types of connections.

Provided a method to construct flat connections from projectively flat ones.

Enhanced understanding of the structure of invariant connections on homogeneous spaces.

Abstract

We show a correspondence between the set of all G-invariant projectively flat connections on a homogeneous apace $M=G/K$, and the one of all {G}^~-invariant flat connections on a homogeneous space {M}^~={G}^~/K, where {G}^~ is a central extension of G.