Infinitesimal isometries of frame bundles with a natural Riemannian metric. II (Q1338404)
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scientific article; zbMATH DE number 697058
| Language | Label | Description | Also known as |
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| English | Infinitesimal isometries of frame bundles with a natural Riemannian metric. II |
scientific article; zbMATH DE number 697058 |
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Infinitesimal isometries of frame bundles with a natural Riemannian metric. II (English)
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31 March 1996
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[For part I, see ibid 43, No. 1, 103-115 (1991: Zbl 0739.53017).] Liftings of vector and tensor fields, esp. Killing fields, on an orientable, complete Riemannian manifold \(M\) to the bundle of frames \(\text{SO} (M)\) are considered. Under certain supplementary conditions on the curvature and on the dimension of \(M\), it is proved that the Lie algebra of Killing fields on \(\text{SO} (M)\) is isomorphic to the three algebras which are defined in an intrinsic way.
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natural lift
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parallel 2-form
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decomposition
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holonomy group
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Killing field
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