Asymptotic expansion of holonomy
Asymptotic expansion of holonomy
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完整律的渐近展开
作者：
E. Grong;P. Pansu
给定一个带连接的主束，我们寻找环的完整度在其长度上的渐近展开式。这个长度是相对于一些黎曼或次黎曼结构定义的。我们能够给出一个与规范的选择无关的渐近公式。我们还展示了我们在次黎曼几何中的结果如何能够为研究欧几里德空间上主束完整展开的情况给出改进的近似。
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.