V2EX holonomy

Holonomy

Definition 定义

holonomy(整体回绕/回路效应;挠率群):在微分几何中,指沿着曲线对向量做“平行移动”后回到起点时,向量可能发生的总体变化;所有闭合回路产生的这种变化所形成的集合,称为挠率群(holonomy group)。在物理中也常用来描述规范场、纤维丛连接等情形下的“绕一圈带来的变换”。

Pronunciation 发音

/hlnmi/

Examples 例句

The holonomy around this loop is not the identity.
绕这条闭合回路的挠率(holonomy)不是恒等变换。

In Riemannian geometry, curvature can be studied via the holonomy group generated by parallel transport along closed curves.
在黎曼几何中,可以通过沿闭合曲线平行移动所生成的挠率群来研究曲率。

Etymology 词源

holonomy 来自希腊语词根组合:**holo-**(λο,意为“整体、全部”)+ -nomy(-νομα/νμο相关,意为“规则、法则、体系”)。字面含义可理解为“整体的规律/整体的约束”,对应其在几何中描述“绕一圈后整体累积效应”的用法。

Related Words 相关词

In Literature 文献与作品

  • Foundations of Differential Geometry(Shoshichi Kobayashi & Katsumi Nomizu)
  • Riemannian Geometry(Manfredo P. do Carmo)
  • A Comprehensive Introduction to Differential Geometry(Michael Spivak)
  • Riemannian Manifolds: An Introduction to Curvature(John M. Lee)
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