Equivariance and Multiplicity for the Scalar Curvature Problem

Abstract

Given (M, g 0) a three-dimensional compact Riemannian manifold, assumed not to be conformally diffeomorphic to the standard unit 3-sphere, and G a compactsubgroup of the conformal group of (M, g 0), we first study conditions for a smooth G-invariant function f to be the scalar curvature of a G-invariant conformalmetric to g 0. Then, extending previous results of Hebeyand Vaugon, we study conditions for f to be the scalarcurvature of at least two conformal metrics to g 0.