Differential Geometric Aspects of Causal Structures

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2018
• Main Author: Makhmali, O.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2018
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/209770
• 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.

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.