Projective differential geometry and geodesic conservation laws in general relativity. I: Projective actions (Q760928)

The Lagrangian structure of the geodesic equation allows an extension of classical projective geometry to one-parameter projective group actions on \(R\times TM\) (where M is the spacetime). We determine all those projective actions which arise by prolongation of one-parameter group actions on \(R\times M\). The relation between projective actions on \(R\times TM\) and the equations of geodesic deviation is developed.