Lifting locally homogeneous geometric structures

TL;DR

This paper establishes algebraic conditions under which locally homogeneous geometric structures modeled on one space can be derived from structures modeled on another, revealing a form of structural transfer.

Contribution

It introduces new algebraic criteria that enable the induction of locally homogeneous structures from different homogeneous models.

Findings

Identifies algebraic conditions for structure induction

Shows structural transfer between different homogeneous spaces

Provides a framework for understanding local homogeneity

Abstract

We prove that under some purely algebraic conditions every locally homogeneous structure modelled on some homogeneous space is induced by a locally homogeneous structure modelled on a different homogeneous space.