Quadratic representation of a submanifold in pseudo-Euclidean space (Q2735676)
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scientific article; zbMATH DE number 1641150
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Quadratic representation of a submanifold in pseudo-Euclidean space |
scientific article; zbMATH DE number 1641150 |
Statements
4 September 2001
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isometric immersion
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pseudo-Riemannian manifold
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quadric representation
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Laplacian operator
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Quadratic representation of a submanifold in pseudo-Euclidean space (English)
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Let \(x\) be an isometric immersion of a pseudo-Riemannian manifold \(M\) in a pseudo-Euclidean space \(E\). The map \(\widetilde x=xx^t\) \((t\) denotes transpose) is called the quadric representation of \(M\). The authors study the map \(\widetilde x\) subject to one of the following conditions: (a) \(\widetilde x\) is of finite type; (b) \(\Delta\widetilde x=B\widetilde x+C\), where \(\Delta\) is the Laplacian operator and \(B\) and \(C\) are two constant matrices.NEWLINENEWLINEFor the entire collection see [Zbl 0954.00038].
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