V2EX hypersurface

Hypersurface

释义 Definition

超曲面:在数学中,指嵌入或浸入在更高维空间中的“维数少 1”的几何对象。比如在三维空间里,二维的曲面(球面、平面)可以看作是超曲面;更一般地,在 \(n\) 维空间中,\((n-1)\) 维的对象称为超曲面。该词在微分几何、偏微分方程与广义相对论中很常见。

发音 Pronunciation (IPA)

/haprsrfs/

例句 Examples

A plane is a hypersurface in three-dimensional space.
平面在三维空间中是一种超曲面。

In general relativity, one often studies a spacelike hypersurface to specify initial data for the evolution of spacetime.
在广义相对论中,人们常研究类空超曲面,用来给出时空演化的初始数据。

词源 Etymology

hypersurface 由 **hyper-**(“超、超过、在更高维度/更高层次”)与 surface(“表面、曲面”)构成,字面意思是“高维的曲面”。它用来强调:对象仍像“表面”那样是“边界/层”,但所在空间的维数更高。

相关词 Related Words

文学与经典著作 Literary Works

  • Robert M. Wald, General Relativity(讨论用于初值问题的类空超曲面等概念)
  • Manfredo P. do Carmo, Riemannian Geometry(涉及超曲面与曲率等几何性质)
  • John M. Lee, Introduction to Smooth Manifolds(以流形语言系统介绍超曲面/子流形)
  • Michael Spivak, A Comprehensive Introduction to Differential Geometry(多卷本中广泛使用 hypersurface 术语)
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