Differential Geometric Aspects of Causal Structures

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 manifold. The local equivalence problem structures on manifolds dimension at least four solved using Cartan's method equivalence, leading to an $\{e\}$-structure over some principal bundle. It shown that these correspond parabolic geometries type $(D_n,P_{1,2})$ and $(B_{n-1},P_{1,2})$, when $n\geq 4$, $(D_3,P_{1,2,3})$. essential invariants determined interpreted geometrically. Several special classes considered including those lift pseudo-conformal referred vanishing Wsf curvature. A twistorial construction for curvature given.