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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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| 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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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862662898157879296 |
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| author | Makhmali, O. |
| author_facet | Makhmali, O. |
| citation_txt | Differential Geometric Aspects of Causal Structures / O. Makhmali // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 71 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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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| first_indexed | 2025-12-07T15:10:08Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-209770 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T15:10:08Z |
| publishDate | 2018 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | 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 |
| spellingShingle | Differential Geometric Aspects of Causal Structures Makhmali, O. |
| title | 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_short | Differential Geometric Aspects of Causal Structures |
| title_sort | differential geometric aspects of causal structures |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/209770 |
| work_keys_str_mv | AT makhmalio differentialgeometricaspectsofcausalstructures |