Asymptotic expansion of holonomy
Author:
Grong Erlend,Pansu Pierre
Abstract
Abstract
Given a principal bundle with a connection, we look for an asymptotic expansion of the holonomy of a loop in terms of its length. This length is defined relative to some Riemannian or sub-Riemannian structure. We are able to give an asymptotic formula that is independent of choice of gauge. We also show how our results from sub-Riemannian geometry can give improved approximations for the case of studying expansions of holonomy of principal bundles over the Euclidean space.
Funder
Norges Forskningsråd
Agence Nationale de la Recherche
Fonds National de la Recherche Luxembourg
Publisher
Walter de Gruyter GmbH
Subject
Applied Mathematics,General Mathematics
Reference28 articles.
1. A theorem on holonomy;Trans. Amer. Math. Soc.,1953
2. A metric characterization of Carnot groups;Proc. Amer. Math. Soc.,2015
3. Holonomy of sub-Riemannian manifolds;Internat. J. Math.,1997
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献