A Criterion for Compatibility of Conformal and Projective Structures

Abstract

In a space-time M, a conformal structure is defined by the distribution of light-cones. Geodesics are traced by freely falling particles, and the collection of all unparameterized geodesics determines the projective structure of M. The article contains a formulation of the necessary and sufficient conditions for these structures to be compatible, i.e. to come from a metric tensor which is then unique up to a constant factor. The theorem applies to all dimensions and signatures. © 2013 The Author(s).