English Dictionary

differential form

名詞

数学 時々

(differential geometry, tensor calculus, sometimes as "differential p-form") A completely antisymmetric tensor (of order p) that is defined on a Riemannian manifold; an expression, derived by applying a formalism to said tensor, that represents an integrand over the manifold.

日本語の意味

微分形式：リーマン多様体上で定義される、完全反対称性を持つp次のテンソル。積分の被積分関数として表現され、微分幾何学やテンソル解析で用いられる。

The exterior derivative of a differential form encodes how the field twists across the manifold.

外微分は、多様体上に定義された完全反対称のp階テンソル（微分形式）が場としてどのようにねじれるかを捉える。

意味（1）

(differential geometry, tensor calculus, sometimes as "differential p-form") A completely antisymmetric tensor (of order p) that is defined on a Riemannian manifold; an expression, derived by applying a formalism to said tensor, that represents an integrand over the manifold.

The notion of differential form combines the concepts of multilinear form (itself an extension of linear form) and smooth function.

differential forms （ plural ）