  We construct novel conformal sigma models in three dimensions. Nonlinear
sigma models in three dimensions are nonrenormalizable in perturbation theory.
We use Wilsonian renormalization group equation method to find the fixed
points. Existence of fixed points is extremely important in this approach to
show the renormalizability. Conformal sigma models are defined as the fixed
point theories of the Wilsonian renormalization group equation. The Wilsonian
renormalization group equation with anomalous dimension coincides with the
modified Ricci flow equation. The conformal sigma models are characterized by
one parameter which corresponds to the anomalous dimension of the scalar
fields. Any Einstein-K\"{a}hler manifold corresponds to a conformal field
theory when the anomalous dimension is $\gamma=-1/2$. Furthermore, we
investigate the properties of target spaces in detail for two dimensional case,
and find the target space of the fixed point theory becomes compact or
noncompact depending on the value of the anomalous dimension.
