Manifolds of Riemannian metrics with prescribed scalar curvature

Introduction. Throughout, M will denote a C 00 compact connected oriented -manifold, ri^.2. Let p:M-+R be a C 00 function,^ the space of C 00 riemannian metrics on M and where R(g) is the scalar curvature of g. As in Ebin [3], a superscript s will denote objects in the corresponding Sobolev space, >w/2+l (one can also treat W 8,p spaces in the same way), and we also allow s= oo so *^ = Jl'. Sign conventions on curvatures are as in Lichnerowicz [10].