Eastwood, Michael GeorgeMatveev, Vladimir2009-12-072009-12-072008Sysmmetries and Overdetermined Systems of Partial Differential Equations / Michael Eastwood and Willard Miller (eds.):pp.339-3509780387738314http://hdl.handle.net/2440/54409We search for Riemannian metrics whose Levi-Civita connection belongs to a given projective class. Following Sinjukov and Mikeš, we show that such metrics correspond precisely to suitably positive solutions of a certain projectively invariant finite-type linear system of partial differential equations. Prolonging this system, we may reformulate these equations as defining covariant constant sections of a certain vector bundle with connection. This vector bundle and its connection are derived from the Cartan connection of the underlying projective structure.enprojective differential geometry; metric connection; tractorBook chapter002008325310.1007/978-0-387-73831-4_16