V2EX normal bundle

Normal Bundle

释义 Definition

(数学/微分几何)法丛/法向量丛:给定一个嵌入到更大空间中的流形(或子流形),在每个点处取“与切空间正交(或互补)”的法向量所组成的向量空间,把这些法空间在全体点上平滑地拼接起来,就得到该子流形的normal bundle。常用于描述子流形在环境空间中的“弯曲方向”。

发音 Pronunciation (IPA)

/nrml bndl/

例句 Examples

The normal bundle describes directions perpendicular to the surface.
法丛描述了与该曲面垂直的方向。

In Riemannian geometry, the normal bundle of an embedded submanifold helps define concepts like the second fundamental form and extrinsic curvature.
在黎曼几何中,嵌入子流形的法丛有助于定义第二基本形式与外在曲率等概念。

词源 Etymology

Normal 源自拉丁语 normalis(“合乎规矩/与直角有关”),在几何里引申为“垂直的、法向的”;bundle 原义为“捆、束”,在数学中指“把每个点上附着的结构(如向量空间)整体组织起来”的“丛”。合起来,normal bundle 就是“由法向方向组成的一束(丛)”。

相关词 Related Words

文学与经典著作中的用例 Literary Works

  • Foundations of Differential Geometry, Vol. 1 Shoshichi Kobayashi & Katsumi Nomizu
  • Riemannian Geometry Manfredo P. do Carmo
  • Differential Geometry of Curves and Surfaces Manfredo P. do Carmo
  • Geometry of Differential Forms Shigeyuki Morita
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