Non-almost periodicity of parallel transports for homogeneous connections
type: Item
instance of: scholarly article
title: Non-almost periodicity of parallel transports for homogeneous connections
zbMATH Open document ID: 1262.83057
author: Johannes Brunnemann
author: Christian Fleischhack
published in: Mathematical Physics, Analysis and Geometry
publication date: 2013-01-04T00:00:00Z
review text: In homogeneous isotropic cosmological models, the classical configuration space is spanned by \(cA\) where \(c\in \mathbb{R}\) and \(A\) is a fixed homogeneous and isotropic connection. In fact, one does not consider these connections themselves but their parallel transports along certain edges. Usually, only straight edges have been taken into account and for such edges the parallel transports are periodic in the scalar \(c\), hence almost periodic. However, the concept of straightness requires a background metric. Therefore, it seems appropiate to consider general, non-straight edges. The main result of this paper proves that these edges, in general, do not lead to almost periodic parallel transports, whence they cannot be extended continuously to the Bohr compactification \(\overline{\mathbb{R}}_{Bohr}\). Technical arguments extend this result to the anisotropic case.
Mathematics Subject Classification ID: 83F05
Mathematics Subject Classification ID: 34C27
Mathematics Subject Classification ID: 53C05
Mathematics Subject Classification ID: 34A26
Mathematics Subject Classification ID: 34C14
Mathematics Subject Classification ID: 83C45
Mathematics Subject Classification ID: 83C05
zbMATH DE Number: 6121941
zbMATH Keywords: parallel transports
zbMATH Keywords: spaces of connections
zbMATH Keywords: almost periodicity
zbMATH Keywords: qualitative theory of ODEs
zbMATH Keywords: loop quantum gravity
zbMATH Keywords: cosmological models
reviewed by: Mircea Crasmareanu
MaRDI profile type: Publication
full work available at URL: s11040-012-9109-7
OpenAlex ID: W2041379535
cites work: Background independent quantum gravity: a status report
cites work: Relating loop quantum cosmology to loop quantum gravity: symmetric sectors and embeddings
cites work: Q5890171
DOI: 10.1007/S11040-012-9109-7
description: scientific article; zbMATH DE number 6121941