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- Die Schouten-Nijenhuis-Klammer ist ein Begriff aus der Differentialgeometrie. Sie bezeichnet ein Typ graduierter Lie-Klammern auf dem Raum der alternierenden Multivektorfelder auf einer differenzierbaren Mannigfaltigkeit. Der Name wird manchmal auch für eine zweite Definition verwendet, die für symmetrische Multivektorfelder gilt. Sie sind benannt nach Jan Schouten und Albert Nijenhuis. (de)
- In differential geometry, the Schouten–Nijenhuis bracket, also known as the Schouten bracket, is a type of graded Lie bracket defined on multivector fields on a smooth manifold extending the Lie bracket of vector fields. There are two different versions, both rather confusingly called by the same name. The most common version is defined on alternating multivector fields and makes them into a Gerstenhaber algebra, but there is also another version defined on symmetric multivector fields, which is more or less the same as the Poisson bracket on the cotangent bundle. It was invented by Jan Arnoldus Schouten (1940, 1953) and its properties were investigated by his student Albert Nijenhuis (1955). It is related to but not the same as the Nijenhuis–Richardson bracket and the Frölicher–Nijenhuis bracket. (en)
- 미분기하학에서, 스하우턴-네이엔하위스 괄호(영어: Schouten–Nijenhuis bracket)는 완전 반대칭 텐서장에 대하여 정의되는 이항 쌍선형 연산이다. 이를 통해, 완전 반대칭 텐서장들은 거스틴해버 대수를 이룬다. (ko)
- 在微分几何中，斯豪滕–奈恩黑斯括号（Schouten–Nijenhuis bracket，国际音标：[ˈsχʌutən]-[ˈnɛiənhœys]），也称为斯豪滕括号，是定义在光滑流形上的场上的一种，推广了向量场的李括号。有两种不同的版本，让人相当不解地是有相同的名字。最通常的版本是定义在交错多重向量场上，使得其成为一个格尔斯滕哈伯代数；但另一个版本定义在对称多重向量场上，这或多或少与余切丛上的泊松括号相同。它由（Jan Arnoldus Schouten）在1940年与1953年发现，其性质为他的学生（Albert Nijenhuis）在1955年研究。它与及弗勒利歇尔－奈恩黑斯括号有联系但不相同。 (zh)
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- Die Schouten-Nijenhuis-Klammer ist ein Begriff aus der Differentialgeometrie. Sie bezeichnet ein Typ graduierter Lie-Klammern auf dem Raum der alternierenden Multivektorfelder auf einer differenzierbaren Mannigfaltigkeit. Der Name wird manchmal auch für eine zweite Definition verwendet, die für symmetrische Multivektorfelder gilt. Sie sind benannt nach Jan Schouten und Albert Nijenhuis. (de)
- 미분기하학에서, 스하우턴-네이엔하위스 괄호(영어: Schouten–Nijenhuis bracket)는 완전 반대칭 텐서장에 대하여 정의되는 이항 쌍선형 연산이다. 이를 통해, 완전 반대칭 텐서장들은 거스틴해버 대수를 이룬다. (ko)
- 在微分几何中，斯豪滕–奈恩黑斯括号（Schouten–Nijenhuis bracket，国际音标：[ˈsχʌutən]-[ˈnɛiənhœys]），也称为斯豪滕括号，是定义在光滑流形上的场上的一种，推广了向量场的李括号。有两种不同的版本，让人相当不解地是有相同的名字。最通常的版本是定义在交错多重向量场上，使得其成为一个格尔斯滕哈伯代数；但另一个版本定义在对称多重向量场上，这或多或少与余切丛上的泊松括号相同。它由（Jan Arnoldus Schouten）在1940年与1953年发现，其性质为他的学生（Albert Nijenhuis）在1955年研究。它与及弗勒利歇尔－奈恩黑斯括号有联系但不相同。 (zh)
- In differential geometry, the Schouten–Nijenhuis bracket, also known as the Schouten bracket, is a type of graded Lie bracket defined on multivector fields on a smooth manifold extending the Lie bracket of vector fields. There are two different versions, both rather confusingly called by the same name. The most common version is defined on alternating multivector fields and makes them into a Gerstenhaber algebra, but there is also another version defined on symmetric multivector fields, which is more or less the same as the Poisson bracket on the cotangent bundle. It was invented by Jan Arnoldus Schouten (1940, 1953) and its properties were investigated by his student Albert Nijenhuis (1955). It is related to but not the same as the Nijenhuis–Richardson bracket and the Frölicher–Nijenhuis (en)
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- Schouten-Nijenhuis-Klammer (de)
- 스하우턴-네이엔하위스 괄호 (ko)
- Schouten–Nijenhuis bracket (en)
- 斯豪滕－奈恩黑斯括号 (zh)
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