V2EX semi-riemannian

Semi-Riemannian

释义 Definition

半黎曼的;半黎曼几何的:指一种带有不定度量(indefinite metric)的几何/度量结构,即度量张量不一定是正定的。它是黎曼几何的推广,常用于描述洛伦兹几何广义相对论中的时空结构。(该词也常写作 semi-Riemanniansemi Riemannian。)

发音 Pronunciation (IPA)

/sma rimnin/

例句 Examples

A semi-Riemannian metric can have both positive and negative lengths.
半黎曼度量的“长度”可能同时出现正号与负号。

In general relativity, spacetime is modeled as a four-dimensional semi-Riemannian manifold with a Lorentzian signature.
在广义相对论中,时空常被建模为具有洛伦兹符号的四维半黎曼流形。

词源 Etymology

semi- 来自拉丁语 semi(“半、部分”),表示“部分地/不完全地”。Riemannian 源自德国数学家 Bernhard Riemann(黎曼) 的姓氏,用于指与黎曼几何相关的结构。合起来 semi-Riemannian 强调:它与黎曼几何密切相关,但度量不再要求“正定”,因此更一般,能覆盖物理学中常见的洛伦兹情形。

相关词 Related Words

文学与经典著作 Notable Works

  • Barrett O’Neill, Semi-Riemannian Geometry With Applications to Relativity(书名即包含该词,是半黎曼几何的经典教材之一)
  • Stephen Hawking & George F. R. Ellis, The Large Scale Structure of Space-Time(讨论以半黎曼/洛伦兹流形表述的时空几何)
  • Robert M. Wald, General Relativity(以半黎曼/洛伦兹几何语言系统阐述广义相对论)
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