Differential Geometric Aspects of Causal Structures
This article is concerned with causal structures, which are defined as a field of tangentially non-degenerate projective hypersurfaces in the projectivized tangent bundle of a manifold. The local equivalence problem of causal structures on manifolds of dimension at least four is solved using Cartan&...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2018 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2018
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/209770 |
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| Cite this: | Differential Geometric Aspects of Causal Structures / O. Makhmali // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 71 назв. — англ. |
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Makhmali, O. 2025-11-26T11:32:46Z 2018 Differential Geometric Aspects of Causal Structures / O. Makhmali // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 71 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 53A55; 58A15; 58A30 arXiv: 1704.02542 https://nasplib.isofts.kiev.ua/handle/123456789/209770 https://doi.org/10.3842/SIGMA.2018.080 This article is concerned with causal structures, which are defined as a field of tangentially non-degenerate projective hypersurfaces in the projectivized tangent bundle of a manifold. The local equivalence problem of causal structures on manifolds of dimension at least four is solved using Cartan's method of equivalence, leading to an {e}-structure over some principal bundle. It is shown that these structures correspond to parabolic geometries of type (Dₙ, P₁,₂) and (Bₙ₋₁, P₁,₂), when n ≥ 4, and (D₃, P₁,₂,₃). The essential local invariants are determined and interpreted geometrically. Several special classes of causal structures are considered, including those that are a lift of pseudo-conformal structures and those referred to as causal structures with vanishing Wsf curvature. A twistorial construction for causal structures with vanishing Wsf curvature is given. This work was carried out under the guidance of Professor N. Kamran, whom I would like to thank greatly for his clear explanation of Cartan’s method of equivalence and for introducing me to the work of Holland and Sparling [33]. His encouragement, help, and support during my PhD made this work possible. I am also very much indebted to Dennis The for the many helpful conversations that we had and for patiently explaining some aspects of parabolic geometry. I thank the anonymous referees for their corrections and suggestions. The funding for this work was provided by McGill University. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Differential Geometric Aspects of Causal Structures Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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| title |
Differential Geometric Aspects of Causal Structures |
| spellingShingle |
Differential Geometric Aspects of Causal Structures Makhmali, O. |
| title_short |
Differential Geometric Aspects of Causal Structures |
| title_full |
Differential Geometric Aspects of Causal Structures |
| title_fullStr |
Differential Geometric Aspects of Causal Structures |
| title_full_unstemmed |
Differential Geometric Aspects of Causal Structures |
| title_sort |
differential geometric aspects of causal structures |
| author |
Makhmali, O. |
| author_facet |
Makhmali, O. |
| publishDate |
2018 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
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Інститут математики НАН України |
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Article |
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This article is concerned with causal structures, which are defined as a field of tangentially non-degenerate projective hypersurfaces in the projectivized tangent bundle of a manifold. The local equivalence problem of causal structures on manifolds of dimension at least four is solved using Cartan's method of equivalence, leading to an {e}-structure over some principal bundle. It is shown that these structures correspond to parabolic geometries of type (Dₙ, P₁,₂) and (Bₙ₋₁, P₁,₂), when n ≥ 4, and (D₃, P₁,₂,₃). The essential local invariants are determined and interpreted geometrically. Several special classes of causal structures are considered, including those that are a lift of pseudo-conformal structures and those referred to as causal structures with vanishing Wsf curvature. A twistorial construction for causal structures with vanishing Wsf curvature is given.
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| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/209770 |
| citation_txt |
Differential Geometric Aspects of Causal Structures / O. Makhmali // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 71 назв. — англ. |
| work_keys_str_mv |
AT makhmalio differentialgeometricaspectsofcausalstructures |
| first_indexed |
2025-12-07T15:10:08Z |
| last_indexed |
2025-12-07T15:10:08Z |
| _version_ |
1850886104282038272 |