V2EX k-form

K-form

释义 Definition

k-形式(k-form):在微分几何与微分形式理论中,指次数为 k 的微分形式(一种可在流形上与有向 k 维“面积/体积元”配对并进行积分的对象)。常见于外微分、斯托克斯定理等内容。(在不同语境下也可能泛指“第 k 阶/第 k 次的形式”。)

发音 Pronunciation

/ke frm/

例句 Examples

A 2-form can be integrated over a surface.
一个 2-形式可以在曲面上进行积分。

On an oriented manifold, a smooth k-form pulls back under a smooth map and its exterior derivative is a (k+1)-form.
在定向流形上,光滑的 k-形式在光滑映射下可以被拉回,而它的外微分是一个 (k+1)-形式。

词源 Etymology

k 是数学里常用的整数记号,表示“次数/维数/阶数”;form 在此指“(微分)形式”。因此 k-form 字面意思就是“次数为 k 的(微分)形式”。

相关词 Related Words

文学与名著示例 Literary Works

  • Calculus on Manifolds(Michael Spivak)
  • Differential Forms in Algebraic Topology(Raoul Bott & Loring W. Tu)
  • The Geometry of Physics: An Introduction(Theodore Frankel)
  • Introduction to Smooth Manifolds(John M. Lee)
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