2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/73639A Riemannian or pseudo-Riemannian (or conformal) structure is conformally Einstein if and only if there is a suitably generic parallel section of a certain vector bundle -- the so-called standard conformal tractor bundle. We show that this characterisation leads to a systematic approach to constructing obstructions to conformally Einstein metrics. Relaxing the requirement that the parallel tractor field be generic gives a natural generalisation of the Einstein equations.proceedings of the 9th International Conference on Differential Geometry and its ApplicationsDifferential GeometryMathematical Physics53A30; 53B20; secondary 53B15text