Lorentzian homogeneous structures with indecomposable holonomy
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916493542817792 |
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| author | Greenwood, Steven Leistner, Thomas |
| author_facet | Greenwood, Steven Leistner, Thomas |
| contents | For a Lorentzian homogeneous space, we study how algebraic conditions on the isotropy group affect the geometry and curvature of the homogeneous space. More specifically, we prove that a Lorentzian locally homogeneous space is locally isometric to a plane wave if it admits an Ambrose--Singer connection with indecomposable, non-irreducible holonomy. This generalises several existing results that require a certain algebraic type of the torsion of the Ambrose--Singer connection and moreover is in analogy to the fact that a Lorentzian homogeneous space with irreducible isotropy has constant sectional curvature. In addition, we prove results about Lorentzian connections with parallel torsion and for 2-symmetric connections. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_17470 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Lorentzian homogeneous structures with indecomposable holonomy Greenwood, Steven Leistner, Thomas Differential Geometry Primary 53C30, Secondary 53C29, 53C50, 53B30 For a Lorentzian homogeneous space, we study how algebraic conditions on the isotropy group affect the geometry and curvature of the homogeneous space. More specifically, we prove that a Lorentzian locally homogeneous space is locally isometric to a plane wave if it admits an Ambrose--Singer connection with indecomposable, non-irreducible holonomy. This generalises several existing results that require a certain algebraic type of the torsion of the Ambrose--Singer connection and moreover is in analogy to the fact that a Lorentzian homogeneous space with irreducible isotropy has constant sectional curvature. In addition, we prove results about Lorentzian connections with parallel torsion and for 2-symmetric connections. |
| title | Lorentzian homogeneous structures with indecomposable holonomy |
| topic | Differential Geometry Primary 53C30, Secondary 53C29, 53C50, 53B30 |
| url | https://arxiv.org/abs/2404.17470 |