چکيده

The aim of this paper is to classify the cohomogeneity one (and zero) conformal actions on the three dimensional Riemannian spaces whose conformal groups are essential, up to orbit equivalence. Among other results, for any such Riemannian space M, the representations of connected Lie groups acting with cohomogeneity one or zero on M are determined in the conformal group of M up to conjugacy and then up to orbit equivalence. Also the orbits are specified up to conformal equivalence.