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A projective geometry is an equivalence class of torsion free connectionssharing the same unparametrised geodesics; this is a basic structure forunderstanding physical systems. Metric projective geometry is concerned withthe interaction of projective and pseudo-Riemannian geometry. We show that theBGG machinery of projective geometry combines with structures known asYang-Mills detour complexes to produce a general tool for generating invariantpseudo-Riemannian gauge theories. This produces (detour) complexes ofdifferential operators corresponding to gauge invariances and dynamics. Weshow, as an application, that curved versions of these sequences give geometriccharacterizations of the obstructions to propagation of higher spins inEinstein spaces. Further, we show that projective BGG detour complexes generateboth gauge invariances and gauge invariant constraint systems for partiallymassless models: the input for this machinery is a projectively invariant gaugeoperator corresponding to the first operator of a certain BGG sequence. We alsoconnect this technology to the log-radial reduction method and extend thelatter to Einstein backgrounds.

Metric projective geometry, BGG detour complexes and partially massless gauge theories