Differential Geometric Aspects of Causal Structures

Symmetry Integrability and Geometry-Methods and Applications

article

Omid Makhmali¹ 

[1] Institute of Mathematics, Polish Academy of Sciences

关键词: causal geometry;    conformal geometry;    equivalence method;    Cartan connection;    parabolic geometry;   

DOI  :  10.3842/SIGMA.2018.080

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown