Year: 2015
Type: article
Abstract: Causal geometries are geometric structures on manifolds for which a (non-degenerate) null cone exists at every point, such that the null cones satisfy a version of Huygen's principle. Causal geometries are a natural generalization of conformal geometries (in non-Euclidean signature). They appear naturally as incidence geometries for projective geometries in three-dimensions, and third-order ordinary differential equations. These share features with conformal geometries: null geodesics exist, as does the Weyl tensor, and there are Raychaudhuri conditions on the null geodesic deviation.
Author: Jonathan Holland
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1024040355