Projective holonomy I: principles and properties
Abstract The aim of this paper and its sequel is to introduce and classify the holonomy algebras of the projective Tractor connection. After a brief historical background, this paper presents and analyses the projective Cartan and Tractor connections, the various structures they can preserve, and th...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Armstrong, Stuart [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2007 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer Science + Business Media B.V. 2007 |
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| Übergeordnetes Werk: |
Enthalten in: Annals of global analysis and geometry - Springer Netherlands, 1983, 33(2007), 1 vom: 12. Juli, Seite 47-69 |
|---|---|
| Übergeordnetes Werk: |
volume:33 ; year:2007 ; number:1 ; day:12 ; month:07 ; pages:47-69 |
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| DOI / URN: |
10.1007/s10455-007-9076-6 |
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| 520 | |a Abstract The aim of this paper and its sequel is to introduce and classify the holonomy algebras of the projective Tractor connection. After a brief historical background, this paper presents and analyses the projective Cartan and Tractor connections, the various structures they can preserve, and their geometric interpretations. Preserved subbundles of the Tractor bundle generate foliations with Ricci-flat leaves. Contact- and Einstein-structures arise from other reductions of the Tractor holonomy, as do U(1) and $$Sp(1, \mathbb{H})$$ bundles over a manifold of smaller dimension. | ||
| 650 | 4 | |a Projective structures | |
| 650 | 4 | |a Complex projective structures | |
| 650 | 4 | |a Holonomy | |
| 650 | 4 | |a Tractor connections | |
| 650 | 4 | |a Cartan connections | |
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Abstract The aim of this paper and its sequel is to introduce and classify the holonomy algebras of the projective Tractor connection. After a brief historical background, this paper presents and analyses the projective Cartan and Tractor connections, the various structures they can preserve, and their geometric interpretations. Preserved subbundles of the Tractor bundle generate foliations with Ricci-flat leaves. Contact- and Einstein-structures arise from other reductions of the Tractor holonomy, as do U(1) and $$Sp(1, \mathbb{H})$$ bundles over a manifold of smaller dimension. © Springer Science + Business Media B.V. 2007 |
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Abstract The aim of this paper and its sequel is to introduce and classify the holonomy algebras of the projective Tractor connection. After a brief historical background, this paper presents and analyses the projective Cartan and Tractor connections, the various structures they can preserve, and their geometric interpretations. Preserved subbundles of the Tractor bundle generate foliations with Ricci-flat leaves. Contact- and Einstein-structures arise from other reductions of the Tractor holonomy, as do U(1) and $$Sp(1, \mathbb{H})$$ bundles over a manifold of smaller dimension. © Springer Science + Business Media B.V. 2007 |
| abstract_unstemmed |
Abstract The aim of this paper and its sequel is to introduce and classify the holonomy algebras of the projective Tractor connection. After a brief historical background, this paper presents and analyses the projective Cartan and Tractor connections, the various structures they can preserve, and their geometric interpretations. Preserved subbundles of the Tractor bundle generate foliations with Ricci-flat leaves. Contact- and Einstein-structures arise from other reductions of the Tractor holonomy, as do U(1) and $$Sp(1, \mathbb{H})$$ bundles over a manifold of smaller dimension. © Springer Science + Business Media B.V. 2007 |
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