\(A_ X\)-operator on complete Riemannian manifolds (Q1081845)
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scientific article; zbMATH DE number 3971665
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | \(A_ X\)-operator on complete Riemannian manifolds |
scientific article; zbMATH DE number 3971665 |
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\(A_ X\)-operator on complete Riemannian manifolds (English)
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1986
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In a Riemannian manifold (M,g), let \(L_ X\) and \(\nabla_ X\) be the Lie and covariant derivations with respect to a Killing vector field X. Then \(A_ X=L_ X-\nabla_ X\) is a skew-symmetric operator field. B. Kostant proved that \(A_ X\) belongs to the holonomy algebra at each point, if M is compact. The present author proves that this fact is also true in a complete non-compact (M,g), under the assumption that X has a finite global norm.
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global scalar product
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Killing vector field
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holonomy algebra
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finite global norm
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