e/Volume form

Information
has gloss	eng: In mathematics, a volume form on a differentiable manifold is a nowhere vanishing differential form of top degree. Thus on a manifold M of dimension n, a volume form is an n-form, a section of the line bundle Ωn(M) = Λn(T&lowast;M), that is nowhere equal to zero. A manifold has a volume form if and only if it is orientable, and orientable manifolds have infinitely many, since multiplying a volume form by a nonvanishing function yields another volume form. On non-orientable manifolds, one may instead define the weaker notion of a density.
lexicalization	eng: volume form
instance of	e/Differential form

Meaning
German
has gloss	deu: Eine Volumenform ist ein mathematisches Objekt, welches zur Integration über Raumbereiche benötigt wird, insbesondere bei der Verwendung spezieller Koordinatensysteme, also ein Spezialfall eines Volumens.
lexicalization	deu: Volumenform
French
has gloss	fra: En géométrie différentielle, une forme volume généralise la notion de déterminant aux variétés différentielles. Elle définit une mesure sur la variété, permet le calcul des volumes généralisés, et la définition générale des orientations.
lexicalization	fra: Forme Volume
Italian
has gloss	ita: In geometria differenziale, una forma di volume è una particolare n-forma differenziale utile a definire una misura su una varietà differenziabile, e quindi un metodo per definire una nozione di volume all'interno di questa.
lexicalization	ita: forma di volume
Chinese
has gloss	zho: 数学中，体积形式提供了函数在不同坐标系（比如球坐标和圆柱坐标）下对体积积分的一种工具。更一般地，一个体积元是流形上一个测度。
lexicalization	zho: 体积形式