Linear natural operators lifting p-vectors to tensors of type (q, 0) on Weil bundles

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• 作者：Jacek Dębecki
• 刊名：Czechoslovak Mathematical Journal
• 出版年：2016
• 出版时间：June 2016
• 年：2016
• 卷：66
• 期：2
• 页码：511-525
• 全文大小：192 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Analysis
  Convex and Discrete Geometry
  Ordinary Differential Equations
  Mathematical Modeling and IndustrialMathematics
  
• 出版者：Springer Netherlands
• ISSN：1572-9141
• 卷排序：66

文摘

We give a classification of all linear natural operators transforming p-vectors (i.e., skew-symmetric tensor fields of type (p, 0)) on n-dimensional manifolds M to tensor fields of type (q, 0) on TAM, where TA is a Weil bundle, under the condition that p ≥ 1, n ≥ p and n ≥ q. The main result of the paper states that, roughly speaking, each linear natural operator lifting p-vectors to tensor fields of type (q, 0) on TA is a sum of operators obtained by permuting the indices of the tensor products of linear natural operators lifting p-vectors to tensor fields of type (p, 0) on TA and canonical tensor fields of type (q − p, 0) on TA.Keywordsnatural operatorWeil bundle