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Statements

Subject Item
dbr:Vector-valued_differential_form
rdf:type
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벡터 값 미분 형식 Vector-valued differential form 向量值微分形式 Vektorwertige Differentialformen
rdfs:comment
数学中，流形 M 上一个向量值微分形式（vector-valued differential form）是 M 上取值于一个向量空间 V 的微分形式。更一般地，它是取值于 M 上某个向量丛 E 的微分形式。通常的微分形式可以视为 R-值微分形式。向量值微分形式是微分几何中的自然对象并有广泛的应用。 In mathematics, a vector-valued differential form on a manifold M is a differential form on M with values in a vector space V. More generally, it is a differential form with values in some vector bundle E over M. Ordinary differential forms can be viewed as R-valued differential forms. An important case of vector-valued differential forms are Lie algebra-valued forms. (A connection form is an example of such a form.) Als Vektorwertige Differentialformen bezeichnet man in der Mathematik eine Verallgemeinerung des Begriffs der Differentialformen auf Funktionen, die jedem Punkt einer Mannigfaltigkeit eine vektorwertige multilineare und alternierende Abbildungen zuordnen. Ein wichtiger Spezialfall bilden sogenannte Lie-Algebra-wertige Differentialformen, die zum Beispiel eine wichtige Anwendung in der Theorie der Zusammenhänge und Krümmung eines Hauptfaserbündels finden. Eine Verallgemeinerung des Konzepts der vektorwertigen Differentialformen sind . 미분기하학에서 벡터 값 미분 형식(vector값微分形式, 영어: vector-valued differential form)의 개념은 미분 형식의 개념의 일종의 일반화이다. 벡터 값 미분 형식은 미분 형식 다발과 임의의 벡터 다발과의 텐서곱 다발의 단면이며, 일종의 "뒤틀린 미분 형식"으로 여겨질 수 있다. 그 위에는 당김과 쐐기곱이 정의되지만, 일반적으로 외미분은 정의되지 않는다.
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dbc:Vector_bundles dbc:Differential_forms
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In mathematics, a vector-valued differential form on a manifold M is a differential form on M with values in a vector space V. More generally, it is a differential form with values in some vector bundle E over M. Ordinary differential forms can be viewed as R-valued differential forms. An important case of vector-valued differential forms are Lie algebra-valued forms. (A connection form is an example of such a form.) 미분기하학에서 벡터 값 미분 형식(vector값微分形式, 영어: vector-valued differential form)의 개념은 미분 형식의 개념의 일종의 일반화이다. 벡터 값 미분 형식은 미분 형식 다발과 임의의 벡터 다발과의 텐서곱 다발의 단면이며, 일종의 "뒤틀린 미분 형식"으로 여겨질 수 있다. 그 위에는 당김과 쐐기곱이 정의되지만, 일반적으로 외미분은 정의되지 않는다. Als Vektorwertige Differentialformen bezeichnet man in der Mathematik eine Verallgemeinerung des Begriffs der Differentialformen auf Funktionen, die jedem Punkt einer Mannigfaltigkeit eine vektorwertige multilineare und alternierende Abbildungen zuordnen. Ein wichtiger Spezialfall bilden sogenannte Lie-Algebra-wertige Differentialformen, die zum Beispiel eine wichtige Anwendung in der Theorie der Zusammenhänge und Krümmung eines Hauptfaserbündels finden. Eine Verallgemeinerung des Konzepts der vektorwertigen Differentialformen sind . 数学中，流形 M 上一个向量值微分形式（vector-valued differential form）是 M 上取值于一个向量空间 V 的微分形式。更一般地，它是取值于 M 上某个向量丛 E 的微分形式。通常的微分形式可以视为 R-值微分形式。向量值微分形式是微分几何中的自然对象并有广泛的应用。
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