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Эта публикация цитируется в 5 научных статьях (всего в 5 статьях)
Differential Geometric Aspects of Causal Structures
Omid Makhmali Institute of Mathematics, Polish Academy of Sciences, 8 Śniadeckich Str., 00-656 Warszawa, Poland
Аннотация:
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 $(D_n,P_{1,2})$ and $(B_{n-1},P_{1,2})$, when $n\geq 4$, and $(D_3,P_{1,2,3})$. 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.
Ключевые слова:
causal geometry; conformal geometry; equivalence method; Cartan connection; parabolic geometry.
Поступила: 25 апреля 2017 г.; в окончательном варианте 23 июля 2018 г.; опубликована 2 августа 2018 г.
Образец цитирования:
Omid Makhmali, “Differential Geometric Aspects of Causal Structures”, SIGMA, 14 (2018), 080, 50 pp.
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/sigma1379 https://www.mathnet.ru/rus/sigma/v14/p80
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